ĐKXĐ: ...
\(\Rightarrow\sqrt{x^2+91}-\sqrt{y^2+91}=\sqrt{y-2}-\sqrt{x-2}+y^2-x^2\)
\(\Leftrightarrow\frac{x^2-y^2}{\sqrt{x^2+91}+\sqrt{y^2+91}}+\frac{x-y}{\sqrt{x-2}+\sqrt{y-2}}+\left(x-y\right)\left(x+y\right)=0\)
\(\Leftrightarrow\left(x-y\right)\left(\frac{x+y}{\sqrt{x^2+91}+\sqrt{y^2+91}}+\frac{1}{\sqrt{x-2}+\sqrt{y-2}}+x+y\right)=0\)
\(\Leftrightarrow x=y\) (ngoặc to luôn dương với \(x;y\ge2\))
Thay vào pt đầu:
\(\sqrt{x^2+91}=\sqrt{x-2}+x^2\)
\(\Leftrightarrow x^2+1-\sqrt{x^2+91}+\sqrt{x-2}-1=0\)
\(\Leftrightarrow\frac{x^4+x^2-90}{x^2+1+\sqrt{x^2+91}}+\frac{x-3}{\sqrt{x-2}+1}=0\)
\(\Leftrightarrow\frac{\left(x-3\right)\left(x+3\right)\left(x^2+10\right)}{x^2+1+\sqrt{x^2+91}}+\frac{x-3}{\sqrt{x-2}+1}=0\)
\(\Leftrightarrow\left(x-3\right)\left(\frac{\left(x+3\right)\left(x^2+10\right)}{x^2+1+\sqrt{x^2+91}}+\frac{1}{\sqrt{x-2}+1}\right)=0\)
\(\Leftrightarrow x=3\Rightarrow y=3\)
