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