\(\sqrt{x+3}+\sqrt{3x+1}=2\sqrt{x}+\sqrt{2x+2}\)
\(\Leftrightarrow\left(\sqrt{x+3}-\sqrt{2x+2}\right)+\left(\sqrt{3x+1}-2\sqrt{x}\right)=0\)
\(\Leftrightarrow\dfrac{\left(x+3\right)-\left(2x+2\right)}{\sqrt{x+3}-\sqrt{2x+2}}+\dfrac{3x+1-4x}{\sqrt{3x+1}-2\sqrt{x}}=0\)
\(\Leftrightarrow\dfrac{1-x}{\sqrt{x+3}-\sqrt{2x+2}}+\dfrac{1-x}{\sqrt{3x+1}-2\sqrt{x}}=0\)
\(\Leftrightarrow\left(\dfrac{1}{\sqrt{x+3}+\sqrt{2x+2}}+\dfrac{1}{\sqrt{3x+1}+2\sqrt{x}}\right)\left(1-x\right)=0\)
Pt \(\dfrac{1}{\sqrt{x+3}+\sqrt{2x+2}}+\dfrac{1}{\sqrt{3x+1}+2\sqrt{x}}=0\) vô no (VT > 0)
=> 1 - x = 0
<=> x = 1 (nhận)