Question

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

Answer 1

x + y - z = 4 and x² + y² + z² = 30
Since ( x + y - z)2 = x2 + y2 + z2 + 2( xy - yz - zx ), we have
(4)2 = 30 + 2( xy - yz - zx )
⇒ 16 = 30 + 2( xy - yz - zx )
⇒ 2( xy - yz - zx ) = -14
⇒ xy - yz - zx = `-14/2` = -7
∴ xy - yz - zx = -7