Question

me ajudem nessa √x-1=x-7

Answer 1

Vamos lá:

$\sqrt{x}-1=x-7\\\sqrt{x}=x-7+1\\\sqrt{x}=x-6\\\left(\sqrt{x}\right)^2=\left(x-6\right)^2\\x=x^{2\:}-12x+6^2\\x=x^{2\:}-12x+36\\x^{2\:}-12x+36-x=0\\x^{2\:}-13x+36=0\\\\a=1\\b=-13\\c=36\\-----\\\Delta =b^2-4ac\\\Delta =13^2-4\cdot 1\cdot 36\\\Delta \:=169-144\\\Delta \:=25\\-----\\x=\frac{-b\pm \sqrt{\Delta }}{2a}\\x=\frac{-\left(-13\right)\pm \sqrt{25}}{2\cdot 1}\\x=\frac{13\pm 5}{2}\\\\x'=\frac{13+5}{2}=9\\x''=\frac{13-5}{2}=4$
------------------------------------
Verificação:

$x=4:\quad \:\sqrt{4}-1=4-7\quad \:\Rightarrow \:\quad \:\mathrm{Falso}\\x=9:\quad \:\sqrt{9}-1=9-7\quad \:\Rightarrow \:\quad \:\mathrm{Verdadero}$

$S=\left\{x\in \mathbb{R}\:ou\:x=9\right\}$
-------------------------------------
Espero ter ajudado!