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

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Solution

Given $2 x + 3 y = 13$ and $x y = 6$

$(2 x + 3 y) = 13$

$\Rightarrow (2 x + 3 y)^{3} = 13^{3}$

$\Rightarrow 8 x^{3} + 27 y^{3} + 18 x y (2 x + 3 y) = 2197$

$\Rightarrow 8 x^{3} + 27 y^{3} + 18 \times 6 \times 13 = 2197$

$\Rightarrow 8 x^{3} + 27 y^{3} + 1404 = 2197$

$∴ 8 x^{3} + 27 y^{3} = 793$

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