Question

Resolva a equação irracional.
X + 2 = $\sqrt{2 x^{2} - 1}$

Answer 1

$x+ 2 = \sqrt{2 x^{2} - 1} \\\\\\( x+ 2 )^2= ( \sqrt{2 x^{2} - 1} )^2 \to\\\\ x^2+4x+4=2 x^{2} - 1\to\\\\ 2 x^{2} - 1- x^{2} -4x-4=0\to\\\\ x^{2} -4x-5=0\\\\Fatorando:\\\\ (x+1)(x-5)=0\\\\ x+1=0\to~~\boxed{x=-1}\\\\ x-5=0\to~~\boxed{x=5}\\\\\\\\ \large\boxed{\boxed{S=\{-1~;~5\}}}$