Question

if x-y=6 and xy=20, find x^3 -y^3

Answer 1

In the above question, it is given that,

The given equation is $x-y=6$

and $xy=20$

Here we have to find $x^{3}-y^{3}$,

Thus, cubing the given equation we get,

$\begin{array}{l}(\mathrm{x}-\mathrm{y})^{3}=\mathrm{x}^{3}-\mathrm{y}^{3}-3 \mathrm{x}^{2} \mathrm{y}+3 \mathrm{xy}^{2}=216 \\=\mathrm{x}^{3}-\mathrm{y}^{3}-3 \mathrm{yx}(\mathrm{x}-\mathrm{y})=216 \\\mathrm{x}^{3}-\mathrm{y}^{3}=216+3(20)(6) \\\mathrm{x}^{3}-\mathrm{y}^{3}=576\end{array}$

Hence the value is 576.