Question

Resolva, em IR, A EQUACÃO √5x+9 = x-1

Answer 1

$\sqrt{5x + 9} = x - 1 \\ \\ ( \sqrt{5x + 9} )^2=(x-1)^2 \\ \\ 5x + 9 = x^2 - 2x + 1 \\ \\ x^2 - 2x -5x +1 - 9 = 0 \\ \\ x^2 -7x - 8 = 0 \\ \Delta = 49 + 32 \\ \\ \Delta = 81 \\ \\ \\ x = \dfrac{7 \pm \sqrt{81}}{2} \\ \\ \boxed{x' = 8} \\ \\ \boxed{x'' = -1}$

Verificação:

$\sqrt{5.8 + 9} = 8-1 \\ \\ 7 = 7 \ \ V$

$\sqrt{5*(-1)+9} = -1 -1 \\ \\ \pm2 = -2 \\ \\ -2 = -2$

S = { 8, -1}