Question

\(\sqrt{x^2+2x}=-2x^2-4x+3\)

Answer 1

\(PT\Leftrightarrow\sqrt{x^2+2x}-1=-2x^2-4x+2\\ \Leftrightarrow\dfrac{x^2+2x-1}{\sqrt{x^2+2x}+1}+2\left(x^2+2x-1\right)=0\\ \Leftrightarrow\left(x^2+2x-1\right)\left(\dfrac{1}{\sqrt{x^2+2x}+1}+2\right)=0\\ \Leftrightarrow x^2+2x-1=0\left(\dfrac{1}{\sqrt{x^2+2x}+1}+2>0\right)\\ \Leftrightarrow x=-1\pm\sqrt{2}\left(\text{thỏa mãn}\right)\)