Question

Giải phương trình :\(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=0\)

Answer 1

ĐK : \(x\ge1\)

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

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

\(\Leftrightarrow\left|\sqrt{x-1}+1\right|+\left|\sqrt{x-1}-1\right|=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-1}+1=0\\\sqrt{x-1}-1=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-1}=-1\left(VL\right)\\\sqrt{x-1}=1\end{matrix}\right.\)

\(\Rightarrow x-1=1\Leftrightarrow x=2\)

Với x = 2 thay vào PT không thỏa mãn

=> PTVN