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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=2197−1404=793
∴ 8x3+27y3=793 (ans)
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