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I have faced a problem simplifying this equation. picture. I tried to solve it this way: picture, but I just can't get the correct answer. This equation is from high school course, so it must have quite a simple solution, so maybe you will be able to help me :)

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Square both sides of $\sqrt{y} + \sqrt{\frac{1}{y}} = 1$ to get $y + 2 + \frac{1}{y} = 1$; this is the quadratic $y^2 + y + 1 = 0$ with roots $y = \frac{2x+1}{x-1} = \frac{-1\pm\sqrt{-5}}{2}$. So there are no real values of $x$ for which the equation holds.

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  • $\begingroup$ Now I get it, thank you :) $\endgroup$
    – Kothas
    Jun 22, 2014 at 16:24
  • $\begingroup$ You're welcome. Don't forget to upvote and/or accept if you think it appropriate. $\endgroup$
    – rogerl
    Jun 22, 2014 at 16:26

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