Question

√x+2 =x

Answer 1

\(\sqrt{x+2}=x\) (ĐK: \(x\ge-2\))

\(\Leftrightarrow x+2=x^2\)

\(\Leftrightarrow-x^2+x+2=0\)

\(\Rightarrow\Delta=1^2-4\cdot\left(-1\right)\cdot2=9>0\)

Vậy phương trình có 2 nghiệm:

\(\left\{{}\begin{matrix}x_1=\dfrac{-1+\sqrt{9}}{2\cdot\left(-1\right)}=-1\left(tm\right)\\x_2=\dfrac{-1-\sqrt{9}}{2\cdot\left(-1\right)}=2\left(tm\right)\end{matrix}\right.\)

Vậy: \(S=\left\{-1;2\right\}\)