Pls solve and answer the question in detail.
Q. If x, y satisfy the equation $y^x=x^y$ and x = 2 y then $\frac{x^2+y^2}{5}=?$

Dear Student,

$$\begin{gathered} \mathit{G}\mathit{i}\mathit{v}\mathit{e}\mathit{n}\mathbf{:} x^y=y^x and x=2y \\ So, {\left(2y\right)}^y=y^{2y} \\ {2}^y\cancel{\times y^y}=y^y\cancel{\times y^y} \left[\mathbf{U}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{ }\mathbf{p}\mathbf{r}\mathbf{o}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{t}\mathbf{y}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{e}\mathbf{x}\mathbf{p}\mathbf{o}\mathbf{n}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{s}\mathbf{:}\mathbf{ }{\mathbf{y}}^{\mathbf{2}}\mathbf{=}\mathbf{y}\mathbf{\times }\mathbf{y}\right] \\ {2}^y=y^y \\ On Compairing, we get \\ y=2 \\ Substituting in x=2y, we get \\ x=2\times 2 \\ x=4 \\ Now, \frac{x^2+y^2}{5} = \frac{16+4}{5}= \frac{20}{5}= 4 \end{gathered}$$
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