The Golden Equation

Algebra Level 3

1+11+x+11+x=x+1x\sqrt{1+\frac{1}{1+x}}+\frac{1}{\sqrt{1+x}} = \sqrt{x}+\frac{1}{\sqrt{x}}

Which of the following is the root of the above equation?

Note: ϕ=5+12\phi=\frac{\sqrt5+1}{2} and denotes the golden ratio.

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