If $2 x + 3 y = 13 a n d x y = 6,$ find the value of $8 x^{3} + 27 y^{3} .$

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Solution

2x + 3y = 13, xy = 6

Cubing both sides,

$(2 x + 3 y)^{3} = (13)^{3} \Rightarrow (2 x)^{3} + (3 y)^{3} + 3 \times 2 x \times 3 y (2 x + 3 y) = 2197 \Rightarrow 8 x^{3} + 27 y^{3} + 18 x y (2 x + 3 y) = 2197 \Rightarrow 8 x^{3} + 27 y^{3} + 18 \times 6 \times 13 = 2197 \Rightarrow 8 x^{3} + 27 y^{3} + 1404 = 2197 \Rightarrow 8 x^{3} + 27 y^{3} = 2197 - 1404 = 793 ∴ 8 x^{3} + 27 y^{3} = 793$

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

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8 x^{3} + 27 y^{3} i s e q u a l t o

8 x^{3} - 27 y^{3} - 2 x + 3 y :

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