Question

x square + y square =53
xy=14 find value of
x cube + y cube

Answer 1

$$\begin{gathered} {\mathrm{x}}^2+{\mathrm{y}}^2=53 \\ \mathrm{xy}=14 \\ {\left(\mathrm{x}+\mathrm{y}\right)}^2={\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{xy} \\ =53+28 \\ =81 \\ \mathrm{x}+\mathrm{y}=\pm 9 \\ \mathrm{So}, \\ {\left(\mathrm{x}+\mathrm{y}\right)}^3={\mathrm{x}}^3+{\mathrm{y}}^3+3\mathrm{xy}\left(\mathrm{x}+\mathrm{y}\right) \\ {9}^3={\mathrm{x}}^3+{\mathrm{y}}^3+3\times 14\times 9\left[\mathrm{taking}\mathrm{x}+\mathrm{y}=9\right] \\ {\mathrm{x}}^3+{\mathrm{y}}^3=351 \\ \mathrm{Similarly}\mathrm{you}\mathrm{can}\mathrm{get}\mathrm{the}\mathrm{value}\mathrm{by}\mathrm{taking}\mathrm{x}+\mathrm{y}=-9 \end{gathered}$$