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Math Help - Find all real numbers x, y and z?

  1. #1
    Super Member fardeen_gen's Avatar
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    Find all real numbers x, y and z?

    Find all real numbers x, y, z such that 1/xy = (x/z) + 1, 1/yz = (y/x) + 1, 1/zx = (z/y) + 1
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by fardeen_gen View Post
    Find all real numbers x, y, z such that 1/xy = (x/z) + 1, 1/yz = (y/x) + 1, 1/zx = (z/y) + 1
    you are just solving 3 equations in 3 unknowns.. you can do it..
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  3. #3
    Newbie Catherine Morland's Avatar
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    From the symmetry of the equations, try x = y = z, which gives (x,y,z)=\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}  },\frac{1}{\sqrt{2}}\right).
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