If x + y + z = 4 and x2 + y2 + z2 = 12, then find xy + yz + xz.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 2.
We know that
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
On putting the given values
⇒ 42 = 12 + 2(xy + yz + zx)
⇒ 16 = 12 + 2(xy + yz + zx)
⇒ 4 = 2(xy + yz + zx)
⇒ xy + yz + zx = 2