If x + y + z = 30, x² + Y² + z² = 460 and x z = y², then find the value of x z?
Given, x + y + z = 20, x² + Y² + z² = 160 and x z = y² We know, (x + y + z) ² = (x² + Y²+ z²) + 2 (x y + y z + x z) or (30) ² = 460 +2 (x y + y z + x z) or (x y +y z + z x) = (900 - 460) =440/2 Or (x y + y z + z x) = 120 Or (x y + y z + y²) = 120 Or y (x + y + z) = 120 Or y x 30 = 120 or y = (120/30) = 4 Therefore, x z = 4² = 16
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