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

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

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Given: 2x + 3y = 13, xy = 6 

Cubing 2x + 3y = 13 both sides, we get 

(2x + 3y)3 = (13)3 

(2x)3 + (3y)3 + 3(2x )(3y) (2x + 3y) = 2197 

8x3 + 27y3 + 18xy(2x + 3y) = 2197 

8x3 + 27y3 + 18 x 6 x 13 = 2197 

8x3 + 27y3 + 1404 = 2197 

8x3 + 27y3 = 2197 – 1404 

8x3 + 27y3 = 793

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