If x + y - z = 4 and x 2 + y 2 + z 2 = 30, then find the value of xy - yz - zx.

By formula, (x + y - z) 2 = x 2 + y 2 + z 2 + 2(xy - yz - zx) Substituting values we get : ⇒ 4 2 = 30 + 2(xy - yz - zx) ⇒ 16 = 30 + 2(xy - yz - zx) ⇒ 2(xy - yz - zx) = 16 - 30 ⇒ 2(xy - yz - zx) = -14 ⇒ xy - yz - zx = -7. Hence, xy - yz - zx = -7.

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Mathematics

If x + y - z = 4 and x² + y² + z² = 30, then find the value of xy - yz - zx.

Expansions

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Answer

By formula,

(x + y - z)² = x² + y² + z² + 2(xy - yz - zx)

Substituting values we get :

⇒ 4² = 30 + 2(xy - yz - zx)

⇒ 16 = 30 + 2(xy - yz - zx)

⇒ 2(xy - yz - zx) = 16 - 30

⇒ 2(xy - yz - zx) = -14

⇒ xy - yz - zx = -7.

Hence, xy - yz - zx = -7.

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Mathematics

If x + y - z = 4 and x² + y² + z² = 30, then find the value of xy - yz - zx.

Expansions

Answer

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If x + y - z = 4 and x2 + y2 + z2 = 30, then find the value of xy - yz - zx.

Expansions

Answer

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