Question

Ao resolvermos a equação abaixo teremos
√x+5 = x - 1

A)4 e -1
B)nenhuma
C)5
D)-1
E)4

Answer 1

$\underbrace{Veja:}$

$\Rightarrow~~\sf \sqrt{x+5}=x-1$

$\Rightarrow~~\sf (\sqrt{x+5})^2=(x-1)^2$

$\Rightarrow~~\sf x+5=(x)^2-2.(x).(1)+(1)^2$

$\Rightarrow~~\sf x+5=x^2-2x+1$

$\Rightarrow~~\sf x^2-2x+1-x-5=0$

$\Rightarrow~~\sf x^2-3x-4=0$

coeficientes:  a = 1,  b = -3,  c = -4

$~~$

Aplicando a fórmula de Bhaskara

$\sf \Delta=b^2-4.a.c$

$\sf \Delta=(-3)^2-4.(1).(-4)$

$\sf \Delta=9+16$

$\sf \Delta=25$

$\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2.a}$

$\sf x=\dfrac{-(-3)\pm\sqrt{25}}{2.(1)}~~\Rightarrow~~x=\dfrac{3\pm 5}{2}$

$\sf x'=\dfrac{3+5}{2}~~\Rightarrow~~x'=\dfrac{8}{2}~~\Rightarrow~~\boxed{\sf x'=4}$

$\sf x''=\dfrac{3-5}{2}~~\Rightarrow~~x''=-\dfrac{2}{2}~~\Rightarrow~~\boxed{\sf x''=-1}$

$~~$

o conjunto solução é: $~~$$\sf S=\left\{4~~;~-1\right\}$

Resposta: Letra A