HMMT February

Algebra Difficulty 4.9 AIME Find the answer

Solve $x=\sqrt{x-\frac{1}{x}}+\sqrt{1-\frac{1}{x}}$ for $x$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

$\frac{1+\sqrt{5}}{2}$ .

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