Question

Gpt: √x(x-1) + √x(x+2) = 2√x²

Answer 1

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

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

\(+,x\ne0\Rightarrow\sqrt{x-1}+\sqrt{x+2}=2\sqrt{x}\Leftrightarrow2x+1+2\sqrt{\left(x-1\right)\left(x+2\right)}=4x\Leftrightarrow2\sqrt{x^2+x-2}=2x-1\Leftrightarrow4x^2+4x-8=4x^2-4x+1\Leftrightarrow8x=9\Leftrightarrow x=\frac{9}{8}\left(tm\right)\) \(+,x=0\Rightarrow0=0\left(tm\right)\)

\(Vay:x=0;x=\frac{9}{8}\)