Question

Giải phương trình : (x-2)(3+x) = \(\sqrt{x\left(x+1\right)}\) -4

Answer 1

ĐK: \(x\ge0;x\le-1\)

\(pt\Leftrightarrow x^2+x-6=\sqrt{x^2+x}-4\)

\(\Leftrightarrow x^2+x-\sqrt{x^2+x}-2=0\)

\(\Leftrightarrow\left(\sqrt{x^2+x}+1\right)\left(\sqrt{x^2+x}-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x^2+x}=-1\left(l\right)\\\sqrt{x^2+x}=2\end{matrix}\right.\)

\(\sqrt{x^2+x}=2\)

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

\(\Leftrightarrow x=\dfrac{-1\pm\sqrt{17}}{2}\left(tm\right)\)