Question

\(2x\sqrt{x^2-x+1}+4\sqrt{3x+1}=2x^2+2x+6\)

Answer 1

\(2x\sqrt{x^2-x+1}+4\sqrt{3x+1}=2x^2+2x+6\Leftrightarrow x^2-x+1-2x\sqrt{x^2-x+1}+x^2+3x+1-4\sqrt{3x+1}+4=0\Leftrightarrow\left(\sqrt{x^2-x+1}-x\right)^2+\left(\sqrt{3x+1}-2\right)^2=0\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x^2-x+1}-x=0\\\sqrt{3x-1}-2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x^2-x+1=x^2\\3x-1=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\x=1\end{matrix}\right.\)Vậy S={1}