Question

\(x-1=\sqrt{x+5}\)

Answer 1

ĐK: x>=-5

\(PT\Leftrightarrow\left(x+5\right)-\sqrt{x+5}-6=0\)

Đặt \(\sqrt{x+5}=t\ge0\)

PT trở thành \(t^2-t-6=0\Leftrightarrow t=3\left(\text{loại }t=-2\text{ vì không thỏa mãn đk}\right)\)

t = 3 suy ra x = 4 (TM)

Vậy x =4

Answer 2

Answer 3

x-1=\(\sqrt{x+5}\)

\(\Leftrightarrow x^2-2x+1=x+5\)

\(\Leftrightarrow x^2-3x-4=0\)

\(\Leftrightarrow\left(x-4\right)\left(x+1\right)\)=0

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-1\end{matrix}\right.\)

vậy ...