Question:
If $3 x-2 y=11$ and $x y=12$, Find the value of $27 x^{3}-8 y^{3}$
Solution:
Given, 3x - 2y = 11, xy = 12
We know that $(a-b)^{3}=a^{3}-b^{3}-3 a b(a+b)$
$(3 x-2 y)^{3}=11^{3}$
$\Rightarrow 27 x^{3}-8 y^{3}-(18 * 12 * 11)=1331$
$\Rightarrow 27 x^{3}-8 y^{3}-2376=1331$
$\Rightarrow 27 x^{3}-8 y^{3}=1331+2376$
$\Rightarrow 27 x^{3}-8 y^{3}=3707$
Hence, the value of $27 x^{3}-8 y^{3}=3707$
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