\(\Leftrightarrow x^2+y^2-2xy+60=35xy-5x^2y^2=5\left(7xy-x^2y^2\right)\)
\(\Leftrightarrow\left(x-y\right)^2+60=\dfrac{5.49}{4}-\dfrac{5}{4}\left(2xy-7\right)^2\)
\(\Leftrightarrow\left[2\left(x-y\right)\right]^2+5\left(2xy-7\right)^2=5.49-60.4=5\)
\(x;y\in Z;2xy-7\ne0;5\left(2xy-7\right)^2\ge5\Rightarrow\left[2\left(x-y\right)\right]^2=0\rightarrow x=y\)
\(\left|\left(2xy-7\right)\right|=1\) \(\left[{}\begin{matrix}2x^2-7=-1;x^2=3\left(l\right)\\2x^2-7=1;x^2=4\left(n\right)\end{matrix}\right.\)\(\Leftrightarrow\left(x;y\right)=\left(\pm2;\pm2\right)\)
\(PT\Leftrightarrow\left(x^2-2xy+y^2\right)+\left(5x^2y^2-35xy+60\right)=0\)
\(\Leftrightarrow\left(x-y\right)^2+5\left(xy-3\right)\left(xy-4\right)=0\)
\(\Leftrightarrow\left(x-y\right)^2=5\left(3-xy\right)\left(xy-4\right)=0\)
Vì \(\left(x-y\right)^2\ge0\forall x;y\) \(\Leftrightarrow5\left(3-xy\right)\left(xy-4\right)\ge0\Rightarrow3\le xy\le4\)
Xét từng giá trị là ra
