ĐKXĐ: $x\geq1$
$\sqrt{x^{2}-x}+\sqrt{x^{2}+x-2}=0$
`<=>`$\sqrt{x(x-1)}+\sqrt{(x-1)(x+2)}=0$
`<=>`$\sqrt{x}.\sqrt{x-1}+\sqrt{x-1}.\sqrt{x+2}=0$
`<=>`$\sqrt{x-1}(\sqrt{x}+\sqrt{x+2})=0$
`<=>`\(\left[ \begin{array}{l}\sqrt{x-1}=0 (1)\\\sqrt{x}+\sqrt{x+2}=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x-1=0 (1)\\\sqrt{x}=-\sqrt{x+2} (vô lí)\end{array} \right.\)
Giải $(1)$:
$x-1=0$
`<=>`$x=1 (t/m)$
Vậy pt có nghiệm $x=1$
