MathLabs

Problem 2

For what real values of xx is x+2x−1+x−2x−1=A\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=A, given (a) A=2A=\sqrt2, (b) A=1A=1, (c) A=2A=2, where square roots are non-negative?
Step 1 of 4: Determine the domain
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2x−1≥0⟹x≥122x-1\ge0\Longrightarrow x\ge\frac12
Detailed analysis

The inner radical requires 2x−1≥02x-1\ge0, so every real solution must satisfy x≥12x\ge\frac12.