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Question

If 2x+3y=13 and xy=6, find the value of 8x3+27y3.

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Solution

2x + 3y = 13, xy = 6

Cubing both sides,

(2x+3y)3=(13)3 (2x)3+(3y)3+3×2x×3y(2x+3y)=2197 8x3+27y3+18xy(2x+3y)=2197 8x3+27y3+18×6×13=2197 8x3+27y3+1404=2197 8x3+27y3=21971404=793 8x3+27y3=793


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