If x + y + z = 0, and x² + y² + z² = 32, then find the value of xy + yz + zx.
Show answer & explanation
Correct answer: A
Explanation
x + y + z = 0
x² + y² + z² = 32
(x + y + z)² = x² + y² + z² + 2(xy + yz + xz)
0² = 32 + 2(xy + yz + xz)
0 = 32 + 2(xy + yz + xz)
2(xy + yz + xz) = −32
xy + yz + xz = −16