Solve sqrt[4]{x}+sqrt{y}=2xx+w*y

$$\sqrt[ 4 ] { x } + \sqrt { y } = 2 x x + w \cdot y$$

Solve for w (complex solution)

$$\left\{\begin{matrix}w=\frac{-2x^{2}+\sqrt{y}+\sqrt[4]{x}}{y}\text{, }&y\neq 0\\w\in \mathrm{C}\text{, }&\left(x=\frac{2^{\frac{3}{7}}e^{\frac{8\pi i}{7}}}{2}\text{ or }x=0\text{ or }x=\frac{2^{\frac{3}{7}}}{2}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$\sqrt[4]{x}+\sqrt{y}=2x^{2}+wy$$

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

$$2x^{2}+wy=\sqrt[4]{x}+\sqrt{y}$$

Subtract 2x^{2} from both sides.

$$wy=\sqrt[4]{x}+\sqrt{y}-2x^{2}$$

The equation is in standard form.

$$yw=-2x^{2}+\sqrt{y}+\sqrt[4]{x}$$

Divide both sides by y.

$$\frac{yw}{y}=\frac{-2x^{2}+\sqrt{y}+\sqrt[4]{x}}{y}$$

Dividing by y undoes the multiplication by y.

$$w=\frac{-2x^{2}+\sqrt{y}+\sqrt[4]{x}}{y}$$

Solve for w

$$\left\{\begin{matrix}w=\frac{-2x^{2}+\sqrt{y}+\sqrt[4]{x}}{y}\text{, }&x\geq 0\text{ and }y>0\\w\in \mathrm{R}\text{, }&\left(x=0\text{ or }x=\frac{2^{\frac{3}{7}}}{2}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$\sqrt[4]{x}+\sqrt{y}=2x^{2}+wy$$

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

$$2x^{2}+wy=\sqrt[4]{x}+\sqrt{y}$$

Subtract 2x^{2} from both sides.

$$wy=\sqrt[4]{x}+\sqrt{y}-2x^{2}$$

The equation is in standard form.

$$yw=-2x^{2}+\sqrt{y}+\sqrt[4]{x}$$

Divide both sides by y.

$$\frac{yw}{y}=\frac{-2x^{2}+\sqrt{y}+\sqrt[4]{x}}{y}$$

Dividing by y undoes the multiplication by y.

$$w=\frac{-2x^{2}+\sqrt{y}+\sqrt[4]{x}}{y}$$