Ta có:\(\left(x^2+1\right)\left(x^2+y^2\right)=4x^2y\)
\(\Leftrightarrow x^4+x^2y^2+x^2+y^2-4x^2y=0\)
\(\Leftrightarrow\left(x^4-2xy+y\right)+x^2y^2-2x^2y+x^2=0\)
\(\Leftrightarrow\left(x^2-y\right)^2+x^2\left(y^2-2y+1\right)=0\)
\(\Leftrightarrow\left(x^2-y\right)^2+x^2\left(y-1\right)^2=0\)
\(\Leftrightarrow\left(x^2-y\right)^2+\left[x\left(y-1\right)\right]^2=0\)
\(\Leftrightarrow x^2-y=0\&x\left(y-1\right)=0\)
\(\Leftrightarrow x^2=y\&\left[x=0hoặc\left(y-1=0\right)\right]\)
\(\Leftrightarrow x=\sqrt{y}\&\left[x=0hoac\left(y=1\right)\right]\)
+)Nếu x = 0 thì y = x2=0
+)Nếu y=1 thì \(x=\sqrt{y}=1\)
Vậy x=0 \(\Leftrightarrow\)y=0
x=1\(\Leftrightarrow\)y=1
