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For which real numbers does the following equation hold?

$$\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=\sqrt{2}$$

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    Two warnings. (1.) After you square, you will get a perfect square inside the radical, and so the radical can be simplified. However, remember that $\sqrt{a^2}$ is $|a|$ and **not** simply $a$. (2.) **Check** that the solution you obtain is a true solution. Squaring an equation could introduce *extraneous* (i.e., fake) solutions that must be discarded.2011-09-13
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    A bit late now, but it would have been better if you had showed us what progress you had made, and where you got stuck, so we could tailor our answers to your needs (and also so it wouldn't leave the impression that you were simply interested in getting someone to do all your work for you).2011-09-13
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    *This question does not show any research effort*2011-09-13
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    For whatever it is worth, the question you have asked is the second problem of the very first IMO in $1959$. (http://www.imo-official.org/problems.aspx)2011-09-13

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