Competition problem — Algebra — Maths Olympiad Prep

Library / /74 of 860

Algebra Difficulty 4.8 AIME Find the answer

Let $x=2001^{1002}-2001^{-1002}$ and $y=2001^{1002}+2001^{-1002}$ . Find $x^{2}-y^{2}$ .

Your answer

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

Solution

-4.

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.