Answer :

Given 2x + 3y = 13


(2x + 3y)3 = 133


Here the identity used is


(a + b)3 = a3 + 3a2b + 3ab2 + b3


(2x + 3y)3 = (2x)3 + 3(2x)23y + 3(2x)(3y)2 + (3y)3


8x3 + 36x2y + 54xy2 + 27y3 = 2197


8x3 + 27y3 + 18xy(2x + 3y) = 2197


8x3 + 27y3 = 2197 – 108 (2x + 3y) ( xy = 6 given)


8x3 + 27y3 = 2197 – 108 × 13


8x3 + 27y3 = 2197 – 1404


8x3 + 27y3 = 793


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