\(ĐK:x+y\ge0;x-y\ge0;x,y\ge0\)
\(PT\left(1\right)\Leftrightarrow\sqrt{x+y}-1+\sqrt{x-y}-\sqrt{x^2-y^2}=0\\ \Leftrightarrow\dfrac{x+y-1}{\sqrt{x+y}+1}+\dfrac{x-y-x^2+y^2}{\sqrt{x-y}+\sqrt{x^2-y^2}}=0\\ \Leftrightarrow\dfrac{x+y-1}{\sqrt{x+y}+1}+\dfrac{\left(y-x\right)\left(x+y-1\right)}{\sqrt{x-y}+\sqrt{x^2-y^2}}=0\\ \Leftrightarrow\left(x+y-1\right)\left(\dfrac{1}{\sqrt{x+y}+1}+\dfrac{y-x}{\sqrt{x-y}+\sqrt{x^2+y^2}}\right)=0\)
\(\Leftrightarrow x+y-1=0\left(\dfrac{1}{\sqrt{x+y}-1}+\dfrac{y-x}{\sqrt{x-y}+\sqrt{x^2+y^2}}>0\right)\)
\(\Leftrightarrow y=x-1\)
Thế vào \(PT\left(2\right)\Leftrightarrow\sqrt{x}+\sqrt{x-1}=1\left(x\ge1\right)\Leftrightarrow\sqrt{x}-1+\sqrt{x-1}=0\)
\(\Leftrightarrow\dfrac{x-1}{\sqrt{x}+1}+\dfrac{x-1}{\sqrt{x-1}}=0\\ \Leftrightarrow\left(x-1\right)\left(\dfrac{1}{\sqrt{x}+1}+\dfrac{1}{\sqrt{x-1}}\right)=0\\ \Leftrightarrow x=1\Leftrightarrow y=0\)
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