Find $8 x^{3} + 27 y^{3}$ , if $2 x + 3 y = 13$ and $x y = 6$ .

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Solution

$2 x + 3 y = 13$ $x y = 6$
$(2 x + 3 y)^{3} = 13^{3}$
$8 x^{3} + 27 y^{3} + 3 \times 4 x^{2} \times 3 y + 3 \times 2 x \times 9 y^{2} = 13^{3}$
$8 x^{3} + 27 y^{3} + 18 x y (2 x + 3 y) = 13^{3}$
$8 x^{3} + 27 y^{3} + 18 (6) (13) = 13^{3}$
$8 x^{3} + 27 y^{3} = 793$

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

If $2 x - 3 y$ = 10 and $x y = 16$ ; find the value of $8 x^{3} - 27 y^{3}$

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x y = 2

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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