ĐKXĐ: \(x\ge1\) \(\sqrt{x+2\sqrt{x-1}}-\sqrt{x-2\sqrt{x-1}}=2\Leftrightarrow\sqrt{x-1+2\sqrt{x-1}+1}-\sqrt{x-1-2\sqrt{x-1}+1}=2\)
\(\Leftrightarrow\left|\sqrt{x-1}+1\right|-\left|\sqrt{x-1}-1\right|=2\)
- Nếu \(1\le x
GPT :
\(\sqrt[4]{x}+\sqrt{x}+\sqrt[4]{1-x}+\sqrt{1-x}=2\sqrt[4]{\frac{1}{2}}+2\sqrt{\frac{1}{2}}\)
GPT :
\(\sqrt[4]{x}+\sqrt{x}+\sqrt[4]{1-x}+\sqrt{1-x}=2\sqrt[4]{\frac{1}{2}}+2\sqrt{\frac{1}{2}}\)
GPT : \(\frac{1}{\sqrt{x+3}+\sqrt{x+2}}+\frac{1}{\sqrt{x+2}+\sqrt{x+1}}+\frac{1}{\sqrt{x+1}+\sqrt{x}}\)
GPT
\(\sqrt{x+2\sqrt{x-1}}-\sqrt{x-2\sqrt{x-1}}=2.\)
GPT : \(\sqrt{\sqrt{x}+1-2\sqrt[4]{x}}+\sqrt{\sqrt{x}+9-6\sqrt[4]{x}}=2\)
GPT:
1, \(6x^2+10x-92+\sqrt{\left(x+70\right)\left(2x^2+4x+16\right)}=0\)
2,\(x+3+\sqrt{1-x^2}=3\sqrt{x+1}+\sqrt{1-x}\)
Gpt: \(\sqrt{x-\sqrt{x^2-1}}+x+\sqrt{x^2+1}=2\)
gpt
\(\frac{x^2}{x-1}+\sqrt{x-1}+\frac{\sqrt{x-1}}{x^2}=\frac{x-1}{x^2}+\frac{1}{\sqrt{x-1}}+\frac{x^2}{\sqrt{x-1}}\)
Gpt \(1-\sqrt{2\left(x^2-x+1\right)}=x-\sqrt{x}\)
