Question

Giải pt:

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

Answer 1

\(\leftrightarrow\sqrt{4x^2-1}-\sqrt{2x^2-x}-\sqrt{2x+1}+\sqrt{x}=0\)

\(\leftrightarrow\sqrt{\left(2x+1\right)\left(2x-1\right)}-\sqrt{x\left(2x-1\right)}-\sqrt{2x+1}+\sqrt{x}=0\)

\(\leftrightarrow\sqrt{2x+1}\left(\sqrt{2x-1}-1\right)-\sqrt{x}\left(\sqrt{2x-1}-1\right)=0\)

\(\leftrightarrow\left(\sqrt{2x+1}-\sqrt{x}\right)\left(\sqrt{2x-1}-1\right)=0\)

\(\leftrightarrow\sqrt{2x+1}-\sqrt{x}=0hoặc\sqrt{2x-1}-1=0\)