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