Solve y^frac{1{m}}+y^-frac{1{m}}=2x

$$y ^ { \frac { 1 } { m } } + y ^ { - \frac { 1 } { m } } = 2 x$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y^{\frac{1}{m}}+y^{-\frac{1}{m}}}{2}\text{, }&y\neq 0\text{ and }m\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }m\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2x=y^{\frac{1}{m}}+y^{-\frac{1}{m}}$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{y^{\frac{1}{m}}+y^{-\frac{1}{m}}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{y^{\frac{1}{m}}+y^{-\frac{1}{m}}}{2}$$

Solve for x

$$x=\frac{y^{\frac{1}{m}}+y^{-\frac{1}{m}}}{2}$$

$$\left(y>0\text{ and }m\neq 0\right)\text{ or }\left(y<0\text{ and }Denominator(\frac{2}{m})\text{bmod}2=1\text{ and }Numerator(m)\text{bmod}2=1\right)$$

Steps for Solving Linear Equation

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

$$2x=y^{\frac{1}{m}}+y^{-\frac{1}{m}}$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{y^{\frac{1}{m}}+y^{-\frac{1}{m}}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{y^{\frac{1}{m}}+y^{-\frac{1}{m}}}{2}$$

Solve for m

$$\left\{\begin{matrix}m\neq 0\text{, }&x=1\text{ and }y=1\\m=\log_{\sqrt{x^{2}-1}+x}\left(y\right)\text{; }m=\log_{-\sqrt{x^{2}-1}+x}\left(y\right)\text{, }&y\neq 1\text{ and }y>0\text{ and }x>1\\m\in \mathrm{R}\text{, }&x=-1\text{ and }Denominator(m)\text{bmod}2=1\text{ and }Numerator(m)\text{bmod}2=1\text{ and }y=-1\end{matrix}\right.$$