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Problem 5 of Second round

Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade

December 14, 2019
algebra

Problem Statement

Let n>1n>1 be a natural number. Find the real values of the parameter aa, for which the equation 1+xn+1−xn=a\sqrt[n]{1+x}+\sqrt[n]{1-x}=a has a single real root.
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