1) Find the value of x' + 8y, if x + 2y = 8 and xy = 6
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· x + 2y = 8. xy = 6. y = 6/x. So x + 12/x = 8. x^2 - 8x + 12 = 0 (x-2)(x-6) = 0. So x=2 and y=3 (or) x=6 and y=1. x^3 + 8y^3 = 8 + 8×27 = 224 (if x=2) (or) x^3 + 8y^3 = 216 + 8×1 = 224 (if x=6) So final answer is 224.
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