ให้ B เป็นเซตของคำตอบทั้งหมดของสมการ

จะได้ว่า $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

|B|={17+4-1 \choose 17}=1140\,

ให้ A เป็นเซตของคำตอบของสมการโดยที่ $x_{1}\leq 3,x_{2}\leq 4,x_{3}\leq 5,x_{4}\leq 8$

จะได้ว่า B-A คือเซตของคำตอบทั้งหมดของสมการที่ $x_{1}>3$ หรือ $x_{/}>4$ หรือ $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

x_{3}>5

หรือ

Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } } Error Too many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below. Request served via cp5021 cp5021, Varnish XID 948251947 Upstream caches: cp5021 int Error: 429, Too many requests (f061ab2) at Thu, 09 Jul 2026 21:27:18 GMT Sensitive client information IP address: 158.108.32.49

ให้ $A_{1}$ เป็นเซตคำตอบของสมการที่ $x_{1}>3$

$A_{2}$ เป็นเซตคำตอบของสมการที่ $x_{2}>4$

$A_{3}$ เป็นเซตคำตอบของสมการที่ $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

x_{3}>5

$Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

A_{4}

เป็นเซตคำตอบของสมการที่

Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } } Error Too many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below. Request served via cp5021 cp5021, Varnish XID 995296373 Upstream caches: cp5021 int Error: 429, Too many requests (f061ab2) at Thu, 09 Jul 2026 21:27:21 GMT Sensitive client information IP address: 158.108.32.49

$\|B-A\|\,$	$=\,$	$A_{1}\cup A_{2}\cup A_{3}\cup A_{4}\,$
	$=\,$	$Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } } Error Too many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below. Request served via cp5021 cp5021, Varnish XID 985597724 Upstream caches: cp5021 int Error: 429, Too many requests (f061ab2) at Thu, 09 Jul 2026 21:27:23 GMT Sensitive client information IP address: 158.108.32.49$
	$Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } } Error Too many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below. Request served via cp5021 cp5021, Varnish XID 997851653 Upstream caches: cp5021 int Error: 429, Too many requests (f061ab2) at Thu, 09 Jul 2026 21:27:23 GMT Sensitive client information IP address: 158.108.32.49$	$+\|A_{1}\cap A_{2}\cap A_{4}\|+\|A_{1}\cap A_{3}\cap A_{4}\|+\|A_{2}\cap A_{3}\cap A_{4}\|-\|A_{1}\cap A_{2}\cap A_{3}\cap A_{4}\|\,$

หา $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

|A_{1}|;x_{1}+x_{2}+x_{3}+x_{4}=17

โดยที่

x_{1}>3

ให้เป็นสมการที่ 1

จาก $x_{1}>3$ นั่นก็คือ $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

x_{1}\geq 4

นั่นเอง

ให้ $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

x_{1}^{'}=x_{1}-4

แทนค่าในสมการที่ 1 ได้

Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } } Error Too many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below. Request served via cp5021 cp5021, Varnish XID 993297497 Upstream caches: cp5021 int Error: 429, Too many requests (f061ab2) at Thu, 09 Jul 2026 21:27:26 GMT Sensitive client information IP address: 158.108.32.49

นั่นคือ $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

x_{1}^{'}+x_{2}+x_{3}+x_{4}=13

โดยที่

x_{1}^{'}\geq 0

ด้วย

ดังนั้น $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

|A_{1}|={13+4-1 \choose 13}\,

หา $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

|A_{2}|;x_{1}+x_{2}+x_{3}+x_{4}=17

โดยที่

x_{2}>4

ให้เป็นสมการที่ 2

จาก $x_{2}>4$ นั่นก็คือ $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too Many Requests (6958218)

x_{2}\geq 5

นั่นเอง

ให้ $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

x_{2}^{'}=x_{2}-5

แทนค่าในสมการที่ 2 ได้

Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } } Error Too many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below. Request served via cp5021 cp5021, Varnish XID 969514241 Upstream caches: cp5021 int Error: 429, Too many requests (f061ab2) at Thu, 09 Jul 2026 21:27:30 GMT Sensitive client information IP address: 158.108.32.49

นั่นคือ $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

x_{1}+x_{2}^{'}+x_{3}+x_{4}=12

โดยที่

Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } } Error Too Many Requests (6958218) If you report this error to the Wikimedia System Administrators, please include the details below. Request served via cp5021 cp5021, Varnish XID 999489989 Upstream caches: cp5021 int Error: 429, Too Many Requests (6958218) at Thu, 09 Jul 2026 21:27:30 GMT Sensitive client information IP address: 158.108.32.49

ด้วย

ดังนั้น $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too Many Requests (6958218)

|A_{2}|={12+4-1 \choose 12}\,

หา $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too Many Requests (6958218)

|A_{3}|;x_{1}+x_{2}+x_{3}+x_{4}=17

โดยที่

Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } } Error Too many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below. Request served via cp5021 cp5021, Varnish XID 995296411 Upstream caches: cp5021 int Error: 429, Too many requests (f061ab2) at Thu, 09 Jul 2026 21:27:32 GMT Sensitive client information IP address: 158.108.32.49

ให้เป็นสมการที่ 3

จาก $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

x_{3}>5

นั่นก็คือ นั่นเอง

ให้ แทนค่าในสมการที่ 3 ได้

นั่นคือ โดยที่ ด้วย

ดังนั้น

หา โดยที่ ให้เป็นสมการที่ 4

จาก นั่นก็คือ นั่นเอง

ให้ แทนค่าในสมการที่ 4 ได้

นั่นคือ โดยที่ ด้วย

ดังนั้น

หา โดยที่ ให้เป็นสมการที่ 5

จาก นั่นก็คือ นั่นเอง

ให้ แทนค่าในสมการที่ 5 ได้

นั่นคือ โดยที่ ด้วย

ดังนั้น

หา โดยที่ ให้เป็นสมการที่ 6

จาก นั่นก็คือ นั่นเอง

ให้ แทนค่าในสมการที่ 6 ได้

นั่นคือ โดยที่ ด้วย

ดังนั้น

หา โดยที่ ให้เป็นสมการที่ 7

จาก นั่นก็คือ นั่นเอง

ให้ แทนค่าในสมการที่ 7 ได้

นั่นคือ โดยที่ $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too Many Requests (6958218)

x_{1}^{'}\geq 0,x_{4}^{'}\geq 0

ด้วย

ดังนั้น $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too Many Requests (6958218)

|A_{1}\cap A_{4}|={4+4-1 \choose 4}\,

หา โดยที่ ให้เป็นสมการที่ 8

จาก นั่นก็คือ นั่นเอง

ให้ แทนค่าในสมการที่ 8 ได้

นั่นคือ โดยที่ ด้วย

ดังนั้น

หา โดยที่ $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

x_{2}>4,x_{4}>8

ให้เป็นสมการที่ 9

จาก นั่นก็คือ นั่นเอง

ให้ แทนค่าในสมการที่ 9 ได้

นั่นคือ $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

x_{1}+x_{2}^{'}+x_{3}+x_{4}^{'}=3

โดยที่

Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } } Error Too many requests (f061ab2) If you report this error to the Wikimedia System Administrators, please include the details below. Request served via cp5021 cp5021, Varnish XID 979538806 Upstream caches: cp5021 int Error: 429, Too many requests (f061ab2) at Thu, 09 Jul 2026 21:27:34 GMT Sensitive client information IP address: 158.108.32.49

ด้วย

ดังนั้น $|A_{2}\cap A_{4}|={3+4-1 \choose 3}\,$

หา $Wikimedia Error * { margin: 0; padding: 0; } body { background: #fff; font: 15px/1.6 sans-serif; color: #333; } .content { margin: 7% auto 0; padding: 2em 1em 1em; max-width: 640px; display: flex; flex-direction: row; flex-wrap: wrap; } .footer { clear: both; margin-top: 14%; border-top: 1px solid #e5e5e5; background: #f9f9f9; padding: 2em 0; font-size: 0.8em; text-align: center; } img { margin: 0 2em 2em 0; } a img { border: 0; } h1 { margin-top: 1em; font-size: 1.2em; } .content-text { flex: 1; } p { margin: 0.7em 0 1em 0; } a { color: #0645ad; text-decoration: none; } a:hover { text-decoration: underline; } code { font-family: sans-serif; } summary { font-weight: bold; cursor: pointer; } details[open] { background: #970302; color: #dfdedd; } .text-muted { color: #777; } @media (prefers-color-scheme: dark) { a { color: #9e9eff; } body { background: transparent; color: #ddd; } .footer { border-top: 1px solid #444; background: #060606; } #logo { filter: invert(1) hue-rotate(180deg); } .text-muted { color: #888; } }$

Error

Too many requests (f061ab2)

|A_{3}\cap A_{4}|;x_{1}+x_{2}+x_{3}+x_{4}=17

โดยที่ ให้เป็นสมการที่ 10

จาก นั่นก็คือ นั่นเอง

ให้ แทนค่าในสมการที่ 10 ได้

นั่นคือ โดยที่ ด้วย

ดังนั้น

และในทำนองเดียวกันสามารถหา ได้ด้วยวิธีเดียวกัน

ซึ่งจะได้

ดังนั้นจะได้ว่า

ดังนั้น แบบ

418531 ภาคต้น 2552/โจทย์ปัญหาการวิเคราะห์เชิงการจัด/เฉลยข้อ 10

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