Prove that equation have infinity reals solutions : $\displaystyle x^2 + y^2 = x^2 y^2 $
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$\displaystyle x^2+y^2-x^2y^2-1=-1$ $\displaystyle (x^2-1)(y^2-1)=1$ Let $\displaystyle x^2-1=a, \ a\in\mathbb{R}, \ a>0\Rightarrow x=\pm\sqrt{a+1}$ Then $\displaystyle y^2-1=\frac{1}{a}\Rightarrow y=\pm\sqrt{\frac{1}{a}+1}$
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