Question

alguien me ayuda con el ejercicio 8 es de despejar X con numeros radicales

Answer 1

Respuesta:

$2\sqrt{6}-\sqrt{2}\left(\sqrt{3}+x\right)=\frac{1}{2}\sqrt{6}\quad :\quad x=\frac{3\sqrt{3}}{2}-\sqrt{3}\quad \left(\mathrm{Decimal}:\quad x=0.86602\dots \right)$

Explicación paso a paso:

$\mathrm{Simplificar\:}\frac{1}{2}\sqrt{6}:\quad \sqrt{\frac{3}{2}}$

$2\sqrt{6}-\sqrt{2}\left(\sqrt{3}+x\right)=\sqrt{\frac{3}{2}}$

$\mathrm{Restar\:}2\sqrt{6}\mathrm{\:de\:ambos\:lados}$

$2\sqrt{6}-\sqrt{2}\left(\sqrt{3}+x\right)-2\sqrt{6}=\sqrt{\frac{3}{2}}-2\sqrt{6}$

Simplificar

$-\sqrt{2}\left(\sqrt{3}+x\right)=\sqrt{\frac{3}{2}}-2\sqrt{6}$

$\mathrm{Dividir\:ambos\:lados\:entre\:}-\sqrt{2}$

$\frac{-\sqrt{2}\left(\sqrt{3}+x\right)}{-\sqrt{2}}=\frac{\sqrt{\frac{3}{2}}}{-\sqrt{2}}-\frac{2\sqrt{6}}{-\sqrt{2}}$

$\sqrt{3}+x=\frac{3\sqrt{3}}{2}$

$\mathrm{Restar\:}\sqrt{3}\mathrm{\:de\:ambos\:lados}$

$\sqrt{3}+x-\sqrt{3}=\frac{3\sqrt{3}}{2}-\sqrt{3}$

$x=\frac{3\sqrt{3}}{2}-\sqrt{3}\\o \mathrm{Decimal}:\quad x=0.86602\dots$

b ) Resolver $\mathrm{\frac{x-\sqrt{2}}{\sqrt{2}}-\sqrt{2}=\sqrt{8}}$

$\mathrm{Simplificar\:}\frac{x-\sqrt{2}}{\sqrt{2}}-\sqrt{2}:\quad \frac{\sqrt{2}\left(x-\sqrt{2}\right)}{2}-\sqrt{2}$

$\mathrm{Simplificar\:}\sqrt{8}:\quad 2\sqrt{2}$

$\frac{\sqrt{2}\left(x-\sqrt{2}\right)}{2}-\sqrt{2}$

$\frac{\sqrt{2}\left(x-\sqrt{2}\right)}{2}-\sqrt{2}+\sqrt{2}=2\sqrt{2}+\sqrt{2}$

$\frac{\sqrt{2}\left(x-\sqrt{2}\right)}{2}=3\sqrt{2}$

$\frac{2\sqrt{2}\left(x-\sqrt{2}\right)}{2}=2\cdot \:3\sqrt{2}$

$\sqrt{2}\left(x-\sqrt{2}\right)=6\sqrt{2}$

$\frac{\sqrt{2}\left(x-\sqrt{2}\right)}{\sqrt{2}}=\frac{6\sqrt{2}}{\sqrt{2}}$

$x-\sqrt{2}+\sqrt{2}=6+\sqrt{2}$

$x=6+\sqrt{2} \\ x=7.41421\dots$