Solve H=sqrt{x+sqrt{2x-1}}+sqrt{x-sqrt{2x-1}}

Solve for H

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

x\geq \frac{1}{2}

Solve for x

\left\{\begin{matrix}x\in \begin{bmatrix}\frac{1}{2},1\end{bmatrix}\text{, }&H=\sqrt{2}\\x=\frac{H^{2}+2}{4}\text{, }&H>\sqrt{2}\\x\geq \frac{1}{2}\text{, }&x\leq 1\text{ and }x\geq \frac{1}{2}\text{ and }-\sqrt{x+\sqrt{2x-1}}-\sqrt{x-\sqrt{2x-1}}\geq 0\text{ and }H=-\sqrt{2}\end{matrix}\right.

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Quiz

Algebra

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