If $3 x + 2 y = 9 a n d x y = 3, f i n d : 27 x^{3} + 8 y^{3}$

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Solution

$27 x^{3} + 8 y^{3} = (3 x)^{3} + (2 y)^{3} = (3 x + 2 y)^{3} - 3.3 x .2 y (3 x + 2 y) = (3 x - 2 y)^{3} - 18 x y (3 x + 2 y) = (9)^{3} - 18 (3) (9) = 729 - 486 = 243$

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