ĐKXĐ: \(x\ge2\)
\(\Leftrightarrow x-2\sqrt{x-1}+\sqrt{x-2}=0\)
\(\Leftrightarrow\frac{x^2-4x+4}{x+2\sqrt{x-1}}+\sqrt{x-2}=0\)
\(\Leftrightarrow\frac{\left(x-2\right)^2}{x+2\sqrt{x-1}}+\sqrt{x-2}=0\)
\(\Leftrightarrow\sqrt{x-2}\left(\frac{\left(x-2\right)\sqrt{x-2}}{x+2\sqrt{x-1}}+1\right)=0\)
\(\Leftrightarrow\sqrt{x-2}=0\Rightarrow x=2\)
Giải PT: \(\sqrt{x+9}=\sqrt{x}+\dfrac{2\sqrt{2}}{\sqrt{x}+1}\)
Giải PT: \(\sqrt{2x+3+\sqrt{x+2}}+\sqrt{2x+2-\sqrt{x+2}}=1+2\sqrt{x+2}\)
Giải PT: \(\sqrt{2x+3+\sqrt{x+2}}+\sqrt{2x+2-\sqrt{x+2}}=1+2\sqrt{x+2}\)
Giải PT: \(\sqrt{2x+3\sqrt{x+2}}+\sqrt{2x+2-\sqrt{x+2}}=1+2\sqrt{x+2}\)
giải pt sau
\(\left(\dfrac{\sqrt{x}-1}{x-2\sqrt{x}+1}-\dfrac{2}{\sqrt{x}}\right):\dfrac{2-\sqrt{x}}{x-1}\)
Giải pt:
\(x^3+\left(x+1\right)\sqrt{x+1}+2\sqrt{2}=\left(x+\sqrt{x+1}+\sqrt{2}\right)^3\)
Giải PT:\(\sqrt{1-\sqrt{x^2-x}}=\sqrt{x}-1\)
Giải PT: \(\sqrt{1-\sqrt{x^2-x}}=\sqrt{x}-1\)
giải pt:\(\sqrt{x-1+2\sqrt{x-2}}-\sqrt{x-1-2\sqrt{x-2}}=1\)
Giải PT: \(\sqrt{1-x}+\sqrt{x^2-3x+2}+\left(x-2\right).\sqrt{\dfrac{x-1}{x-2}}=3\)
