Question
If x + y + z = 20, x² + Y² + z² = 160 and x z = y²,
then find the value of x z?Solution
Given, x + y + z = 20, x² + Y² + z² = 160 and x z = y² We know, (x + y + z) ² = (x² + Y²+ z²) + 2 x (x y + y z + x z) or (20) ² = 160 +2 x (x y + y z + x z) or (x y + + z x) = (400 - 160) =240/2 Or (x y + y z + z x) = 120 Or (x y + y z + y²) = 120 Or y (x + y + z) = 120 Or y x 20 = 120 or y = (120/20) = 6 Therefore, x z = 6² = 36
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