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