Question

If x + y + z = 12 and xy + yz + zx = 27; find x² + y² + z².

Answer 1

(x + y + z)² = (12)²
⇒ x² + y² + z² + 2xy + 2yz + 2zx = 144
⇒ x² + y² + z² + 2(xy + yz + zx) = 144
⇒ x² + y² + z² + 2(27) = 144
⇒ x² + y² + z² 
= 144 - 54
= 90.