Question

Giải pt:

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

Em cảm ơn ạ.

Answer 1

Đk \(x\ge0\)

Pt \(\Leftrightarrow\dfrac{2x+1-3x}{\sqrt{2x+1}+\sqrt{3x}}=x-1\)

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

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

\(\Leftrightarrow1-x=0\)( vì \(\dfrac{1}{\sqrt{2x+1}+\sqrt{3x}}+1>0\) với mọi \(x\ge0\))

\(\Leftrightarrow x=1\)

Vậy S={1}