Question

Equação irracional 
$\sqrt{5x+9}=x-1$

Answer 1

$( \sqrt{5x+9}) ^2 = (x-1)^2 5x + 9 = x^2-2x+1 x^2-7x-8=0 (x+1)(x-8)=0$

Logo as raízes são x = -1 e x = 8.

Espero ter ajudado!!!!

Answer 2

$\sqrt{5x+9}=x-1 \\ \\ (\sqrt{5x+9})^2=(x-1)^2 \\ \\ 5x+9=x^2-2x+1 \\ \\ x^2-7x-8=0 \\ \\ \Delta=(-7)^2-4.1.(-8)=49+32=81 \\ \\ x=\frac{7+-\sqrt{81}}{2}=\frac{7+-9}{2} \\ \\ x_1=\frac{-2}{1}=-1 \\ \\ x_2=\frad{16}{2}=8$