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Math Help - Infinity reals solutions

  1. #1
    Super Member dhiab's Avatar
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    Infinity reals solutions

    Prove that equation have infinity reals solutions :
     <br />
x^2 + y^2 = x^2 y^2 <br /> <br />
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  2. #2
    MHF Contributor red_dog's Avatar
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    x^2+y^2-x^2y^2-1=-1

    (x^2-1)(y^2-1)=1

    Let x^2-1=a, \ a\in\mathbb{R}, \ a>0\Rightarrow x=\pm\sqrt{a+1}

    Then y^2-1=\frac{1}{a}\Rightarrow y=\pm\sqrt{\frac{1}{a}+1}
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