Competition problem — Algebra — Maths Olympiad Prep

Library / /179 of 860

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

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

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.