Question

Giải phương trình: \(\sqrt{x+2\sqrt{x}-1}=2\)

Answer 1

ĐKXĐ : \(x\ge\sqrt{2}-1\)

P/t \(\Leftrightarrow x+2\sqrt{x}-1=4\)

\(\Leftrightarrow x+2\sqrt{x}-5=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1+\sqrt{6}\left(tm\right)\\x=-1-\sqrt{6}\left(L\right)\end{matrix}\right.\)
Vậy ... 

Answer 2

Sửa đề: \(\sqrt{x^2+2\sqrt{x-1}}=2\)

\(\Leftrightarrow\left|\sqrt{x-1}+1\right|=2\)

=>căn(x-1)+1=2

=>căn(x-1)=1

=>x-1=1

hay x=2