Question

Căn(x+3) + căn(3x+1)= căn(4x) +căn(2x+2).Mọi người giúp e với huhu :(

Answer 1

ĐKXĐ: \(x\ge0\)

\(\Leftrightarrow\sqrt{4x}-\sqrt{3x+1}+\sqrt{2x+2}-\sqrt{x+3}=0\)

\(\Leftrightarrow\frac{x-1}{\sqrt{4x}+\sqrt{3x+1}}+\frac{x-1}{\sqrt{2x+2}+\sqrt{x+3}}=0\)

\(\Leftrightarrow\left(x-1\right)\left(\frac{1}{\sqrt{4x}+\sqrt{3x+1}}+\frac{1}{\sqrt{2x+2}+\sqrt{x+3}}\right)=0\)

\(\Rightarrow x=1\)