Question

giải pt

a.\(\sqrt{x}-\sqrt{x\left(x+2\right)}=0\)

 b.\(\sqrt{x^2-1}-\sqrt{x-1}=0\)

Answer 1

a. ĐKXĐ: \(x\ge0\)

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

\(\Rightarrow x=x\left(x+2\right)\Leftrightarrow x=x^2+2x\)\(\Rightarrow\left[{}\begin{matrix}x=-1\left(KTM\right)\\x=0\left(TM\right)\end{matrix}\right.\)

b. ĐKXĐ: \(x\ge1\)

\(\sqrt{x^2-1}-\sqrt{x-1}=0\Leftrightarrow\sqrt{x^2-1}=\sqrt{x-1}\)

\(\Rightarrow x^2-1=x-1\Leftrightarrow\left[{}\begin{matrix}x=1\left(TM\right)\\x=0\left(KTM\right)\end{matrix}\right.\)