Question

RESOLVER LA SUIGUIENTE ECUACION :)

Answer 1

RESOLUCIÓN :

$\sqrt{2\sqrt{x+1}}=\sqrt{3x-5}$

$\left(\sqrt{2\sqrt{x+1}}\right)^2=\left(\sqrt{3x-5}\right)^2$

$2\sqrt{x+1}=3x-5$

$\left(2\sqrt{x+1}\right)^2=\left(3x-5\right)^2$

$4x+4=9x^2-30x+25$

$4x+4=9x^2-30x+25$

$9x^2-34x+21=0$

FACTORIZAR :

$\left(x-3\right)\left(9x-7\right)=0$

$x1= \frac{7}{9} x2 =3$

COMPROBAR:

$\mathrm{Sustituir}\quad x=\frac{7}{9}:\quad \sqrt{2\sqrt{\frac{7}{9}+1}}=\sqrt{3\frac{7}{9}-5}\quad \Rightarrow \quad \mathrm{Falso}$

$\mathrm{Sustituir}\quad x=3:\quad \sqrt{2\sqrt{3+1}}=\sqrt{3\cdot \:3-5}\quad \Rightarrow \quad \mathrm{Verdadero}$

RESPUESTA :

$\boxed{\boxed{x =3}}}}$