Question

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

Answer 1

Given x + y + x = p and xy ++ yz + zx = q
(x + y + x)² 
= x² + y² + z² + 2xy + 2yz + 2zx
⇒ x² + y² + z²
= (x + y + z)² - 2xy + 2yz + 2zx
⇒ x² + y² + z² 
= (x + y + z)² - 2(xy + yz + zx)
⇒ x²+ y² + z²
= (p)² - 2(q)
⇒ x² + y² + z²
= p² - 2q.