Question

If x – y = c, z – x = b, y – z = a, a2 + b2 + c2 =25, then the value of x2 + y2 + z2– xy – yz – zx is equal to

Answer 1

⠀⠀⠀⠀ $\purple{\mathbb{ANSWER}}$

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To find:-

x² + y² + z²– xy – yz – zx

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Given:-

x – y = c, z – x = b, y – z = a

a²+b²+c²=25

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a² + b²+ c² = 25

(y – z)² + (z – x)² + (x – y)² = 25

y² + z² -2yz + z² + x² -2zx x² + y² -2xy = 25

2x² +2y² + 2z² - 2xy -2yz -2zx = 25

2(x² +y² + z² - xy - yz - zx) = 25

x² +y² + z² - xy - yz - zx = 25/2

x² +y² + z² - xy - yz - zx = 12.5

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x² +y² + z² - xy - yz - zx = 12.5

Answer 2

Hello,

$\large{\underline{\underline{\bold{\red{\sf{Given:}}}}}}$

• a²+b²+c²=25

_________________

$\large{\underline{\underline{\bold{\red{\sf{Solution}}}}}}$

➥a² + b²+ c² = 25

➥(y – z)² + (z – x)² + (x – y)² = 25

➥y² + z² -2yz + z² + x² -2zx x² + y² -2xy = 25

➥2x² +2y² + 2z² - 2xy -2yz -2zx = 25

➥2(x² +y² + z² - xy - yz - zx) = 25

➥x² +y² + z² - xy - yz - zx = 25/2

➥x² +y² + z² - xy - yz - zx = 12.5 ..

Hope it helps uh !