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Find all rational numbers x

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June 29, 2011

Problem Statement

Let a≥0a \geq 0 be a natural number. Determine all rational xx, so that 1+(a−1)x3=1+(a−1)x\sqrt{1+(a-1)\sqrt[3]x}=\sqrt{1+(a-1)\sqrt x} All occurring square roots, are not negative.
Note. It seems the set of natural numbers = N={0,1,2,…}\mathbb N = \{0,1,2,\ldots\} in this problem.
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