Question

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

giải pt

Answer 1

ĐK: \(x\ge\dfrac{1}{2}\)

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

\(\Leftrightarrow\left\{{}\begin{matrix}x+1\ge0\\2x-1=\left(x+1\right)^2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\x^2=-2\end{matrix}\right.\)

\(\Rightarrow\) Phương trình vô nghiệm

Answer 2

\(\sqrt{2x-1}-x-1=0\) (1)

ĐKXĐ: \(x\ge\dfrac{1}{2}\)

(1) \(\Rightarrow2x-1=\left(x+1\right)^2\)

\(\Leftrightarrow2x-1-x^2-2x-1=0\)

\(\Leftrightarrow-x^2-2=0\)

\(\Rightarrow\)PT vô nghiệm