Question

if 2x + 3y = 13 and xy = 6, find value of 8x cube + 27 y cube

Answer 1

8x^3 + 27y^3
=(2x)^3 + (3y)^3
From a^3 + b^3 = (a + b) (a^2 - ab + b^2) , where a = 2x and b = 3y
Therefore,
(2x)^3 + (3y)^3 = (2x + 3y) (4x^2 - 6xy + 9y^2)
= 13 (4x^2 + 9y^2 - 36)
Squaring 2x + 3y = 13
We get,
4x^2 + 9y^2 +12xy = 169
Therefore, 4x^2 + 9y^2 = 169 - 72
= 97
Putting value in earlier equation, we get,
8x^3 + 27y^3 = 13 (97 - 36)
= 13 * 61
= 793 Answer.....
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Answer 2

Hope it will help you