Question

condição de existencia.
log4(x+x2)=1/2

Answer 1

$log\ _4(x+x^2)=\frac{1}{2}\\\\ 4^(\frac{1}{2}^)=x+x^2\\\\ \sqrt{4}=x+x^2\\\\ 2=x+x^2\\\\ x^2+x-2=0\\\\ \Delta=1+8\\\\ \boxed{\Delta=9}$

$x'=1\\\\ x''=-2$

vamos substituir

$x+x^2>0\\\\ 1+1^2>0\\\\ 1+1>0\\\\ \boxed{2>0}$

$x+x^2>0\\\\ -2+(-2)^2>0\\\\ -2+4>0\\\\ \boxed{2>0}$

A solução é 1 e -2.