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Question

Find the value of 27x3+8y3, if

(i) 3x + 2y = 14 and xy = 8

(ii) 3x + 2y = 20 and xy = 149

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Solution

(i) 3x + 2y = 14 and xy = 8

Cubing both sides,

(3x+2y)3=(14)3 (3x)3+(2y)3+3×3x×2y(3x+2y)=2744 27x3+8y3+18xy(3x+2y)=2744 27x3+9y3+18×8×14=2744 27x3+8y3+2016=2744 27x3+8y3=27442016=728(ii) 3x+2y=20 and xy=149Cubing both sides(3x+2y)3=(20)3 (3x)3+(2y)3+3×3x×2y(3x+2y)=8000 27x3+8y3+8×2xy(3x+2y)=8000 27x3+8y3+18×149×20=8000 27x3+8y3+560=8000 27x3+8y3=8000560=7440 27x3+8y3=7440


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