Solve (1)x^5+y^5=5ax^2y^2

$$( 1 ) x ^ { 5 } + y ^ { 5 } = 5 a x ^ { 2 } y ^ { 2 }$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x^{5}+y^{5}}{5\left(xy\right)^{2}}\text{, }&y\neq 0\text{ and }x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$5ax^{2}y^{2}=1x^{5}+y^{5}$$

Reorder the terms.

$$5ax^{2}y^{2}=x^{5}+y^{5}$$

The equation is in standard form.

$$5x^{2}y^{2}a=x^{5}+y^{5}$$

Divide both sides by 5x^{2}y^{2}.

$$\frac{5x^{2}y^{2}a}{5x^{2}y^{2}}=\frac{x^{5}+y^{5}}{5x^{2}y^{2}}$$

Dividing by 5x^{2}y^{2} undoes the multiplication by 5x^{2}y^{2}.

$$a=\frac{x^{5}+y^{5}}{5x^{2}y^{2}}$$

Divide x^{5}+y^{5} by 5x^{2}y^{2}.

$$a=\frac{x^{5}+y^{5}}{5\left(xy\right)^{2}}$$