Resolver {left(sqrt{frac{yx/545/2x/455/5555{left(z^2right)^frac{x{zsqrt{51}}}}}{z}}right)}^2=50000

$${ \left( \sqrt{ \frac{ \frac{ \frac{ \frac{ \frac{ yx }{ 545 } }{ 2x } }{ 455 } }{ 5555 { \left( { z }^{ 2 } \right) }^{ \frac{ x }{ z \sqrt{ 51 } } } } }{ z } } \right) }^{ 2 } =50000$$

Resolver y

$$y=137750112500000z\left(z^{2}\right)^{\frac{\sqrt{51}x}{51z}}$$

$$z\neq 0\text{ and }x\neq 0$$

Pasos para resolver unha ecuación lineal

Expresa \frac{\frac{\frac{\frac{\frac{yx}{545}}{2x}}{455}}{5555\left(z^{2}\right)^{\frac{x}{z\sqrt{51}}}}}{z} como unha única fracción.

$$\left(\sqrt{\frac{\frac{\frac{\frac{yx}{545}}{2x}}{455}}{5555\left(z^{2}\right)^{\frac{x}{z\sqrt{51}}}z}}\right)^{2}=50000$$

Expresa \frac{\frac{yx}{545}}{2x} como unha única fracción.

$$\left(\sqrt{\frac{\frac{\frac{yx}{545\times 2x}}{455}}{5555\left(z^{2}\right)^{\frac{x}{z\sqrt{51}}}z}}\right)^{2}=50000$$

Anula x no numerador e no denominador.

$$\left(\sqrt{\frac{\frac{\frac{y}{2\times 545}}{455}}{5555\left(z^{2}\right)^{\frac{x}{z\sqrt{51}}}z}}\right)^{2}=50000$$

Multiplica 2 e 545 para obter 1090.

$$\left(\sqrt{\frac{\frac{\frac{y}{1090}}{455}}{5555\left(z^{2}\right)^{\frac{x}{z\sqrt{51}}}z}}\right)^{2}=50000$$

Racionaliza o denominador de \frac{x}{z\sqrt{51}} mediante a multiplicación do numerador e o denominador por \sqrt{51}.

$$\left(\sqrt{\frac{\frac{\frac{y}{1090}}{455}}{5555\left(z^{2}\right)^{\frac{x\sqrt{51}}{z\left(\sqrt{51}\right)^{2}}}z}}\right)^{2}=50000$$

O cadrado de \sqrt{51} é 51.

$$\left(\sqrt{\frac{\frac{\frac{y}{1090}}{455}}{5555\left(z^{2}\right)^{\frac{x\sqrt{51}}{z\times 51}}z}}\right)^{2}=50000$$

Factoriza as expresións que aínda non o están en \frac{x\sqrt{51}}{z\times 51}.

$$\left(\sqrt{\frac{\frac{\frac{y}{1090}}{455}}{5555\left(z^{2}\right)^{\frac{\sqrt{51}x}{51z}}z}}\right)^{2}=50000$$

Anula \sqrt{51} no numerador e no denominador.

$$\left(\sqrt{\frac{\frac{\frac{y}{1090}}{455}}{5555\left(z^{2}\right)^{\frac{x}{\sqrt{51}z}}z}}\right)^{2}=50000$$

Calcula \sqrt{\frac{\frac{\frac{y}{1090}}{455}}{5555\left(z^{2}\right)^{\frac{x}{\sqrt{51}z}}z}} á potencia de 2 e obtén \frac{\frac{\frac{y}{1090}}{455}}{5555\left(z^{2}\right)^{\frac{x}{\sqrt{51}z}}z}.

$$\frac{\frac{\frac{y}{1090}}{455}}{5555\left(z^{2}\right)^{\frac{x}{\sqrt{51}z}}z}=50000$$

Expresa \frac{\frac{\frac{y}{1090}}{455}}{5555\left(z^{2}\right)^{\frac{x}{\sqrt{51}z}}z} como unha única fracción.

$$\frac{\frac{y}{1090}}{455\times 5555\left(z^{2}\right)^{\frac{x}{\sqrt{51}z}}z}=50000$$

Multiplica 455 e 5555 para obter 2527525.

$$\frac{\frac{y}{1090}}{2527525\left(z^{2}\right)^{\frac{x}{\sqrt{51}z}}z}=50000$$

Expresa \frac{\frac{y}{1090}}{2527525\left(z^{2}\right)^{\frac{x}{\sqrt{51}z}}z} como unha única fracción.

$$\frac{y}{1090\times 2527525\left(z^{2}\right)^{\frac{x}{\sqrt{51}z}}z}=50000$$

Multiplica 1090 e 2527525 para obter 2755002250.

$$\frac{y}{2755002250\left(z^{2}\right)^{\frac{x}{\sqrt{51}z}}z}=50000$$

A ecuación está en forma estándar.

$$\frac{\left(z^{2}\right)^{-\frac{x}{\sqrt{51}z}}}{2755002250z}y=50000$$

Divide ambos lados entre \frac{1}{2755002250}\left(z^{2}\right)^{-x\left(\sqrt{51}\right)^{-1}z^{-1}}z^{-1}.

$$\frac{\frac{\left(z^{2}\right)^{-\frac{x}{\sqrt{51}z}}}{2755002250z}y\times 2755002250z}{\left(z^{2}\right)^{-\frac{x}{\sqrt{51}z}}}=\frac{50000\times 2755002250z}{\left(z^{2}\right)^{-\frac{x}{\sqrt{51}z}}}$$

A división entre \frac{1}{2755002250}\left(z^{2}\right)^{-x\left(\sqrt{51}\right)^{-1}z^{-1}}z^{-1} desfai a multiplicación por \frac{1}{2755002250}\left(z^{2}\right)^{-x\left(\sqrt{51}\right)^{-1}z^{-1}}z^{-1}.

$$y=\frac{50000\times 2755002250z}{\left(z^{2}\right)^{-\frac{x}{\sqrt{51}z}}}$$

Divide 50000 entre \frac{1}{2755002250}\left(z^{2}\right)^{-x\left(\sqrt{51}\right)^{-1}z^{-1}}z^{-1}.

$$y=137750112500000z\left(z^{2}\right)^{\frac{\sqrt{51}x}{51z}}$$

Resolver x

$$\left\{\begin{matrix}x\neq 0\text{, }&\left(y=-137750112500000\text{ and }z=-1\right)\text{ or }\left(y=137750112500000\text{ and }z=1\right)\\x=-\frac{\sqrt{51}\left(\ln(\frac{z}{y})+\ln(137750112500000)\right)z}{\ln(z^{2})}\text{, }&\left(y\neq 137750112500000z\text{ and }z>0\text{ and }y>0\text{ and }z\neq 1\right)\text{ or }\left(y\neq 137750112500000z\text{ and }z<0\text{ and }y<0\text{ and }z\neq -1\right)\end{matrix}\right.$$