tag:blogger.com,1999:blog-2400513859305780710.post7491267775329089551..comments2023-04-04T07:53:53.789-07:00Comments on Mathematical Food For Thought: Mission Accomplished! Topic: Algebra. Level: AIME.Jeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-2400513859305780710.post-74814995981004362612006-06-18T08:12:08.000-07:002006-06-18T08:12:08.000-07:00We wish to showx^6 - 2x^5 + 2x^3 - 2x + 1 \ge 0Thi...We wish to show<br><br>x^6 - 2x^5 + 2x^3 - 2x + 1 \ge 0<br><br>This factors as<br><br>(x-1)^2 (x^4 - x^2 + 1) \ge (x-1)^2 (x^4 - 2x^2 + 1) \ge (x-1)^2 (x^2 - 1)^2 \ge 0<br><br>QED.<br><br>(India MO problems are a little on the easy side, as far as MO problems go...)QCnoreply@blogger.com