Question

Giải các pt sau:

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

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

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

Answer 1

\(\text{Đ}K:\text{ }x\ge\frac{1}{2}\)

\(1\Leftrightarrow2x+2\sqrt{x^2-2x+1}=2\Leftrightarrow x+\sqrt{\left(x-1\right)^2}=1\Leftrightarrow x+\left|x-1\right|=1\)

\(+,x\ge1\Rightarrow\left|x-1\right|=x-1\Rightarrow2x-1=1\Leftrightarrow x=1\left(tm\right)\)

\(+,x< 1\Rightarrow\left|x-1\right|=1-x\Rightarrow1=1\left(\text{đ}ung\right)\Rightarrow\frac{1}{2}\le\text{ }x< 1\)

\(Vaay:\frac{1}{2}\le x\le1\)