tag:blogger.com,1999:blog-2400513859305780710.post4791237098081933555..comments2023-04-04T07:53:53.789-07:00Comments on Mathematical Food For Thought: Mix it Up. Topic: Polynomials/Inequalities. Level: Olympiad.Jeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-2400513859305780710.post-24458982564511870772005-11-25T13:29:42.000-08:002005-11-25T13:29:42.000-08:00......which can be rearranged to (image) which cle.........which can be rearranged to (image)<br><br> which clearly cannot hold if all the roots are real. QED.<br><br>Can you explain how you rearranged?1234567890noreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-67290690070099881582005-11-25T13:35:53.000-08:002005-11-25T13:35:53.000-08:00Nice solution to #1!Nice solution to #1!chess64noreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-32868673911355402432005-11-25T13:44:19.000-08:002005-11-25T13:44:19.000-08:00@1234567890: Put all the terms on the LHS, multipl...@1234567890: Put all the terms on the LHS, multiply by 2, and rearrange things so you get something like this - a^2-2ab+b^2 = (a-b)^2 for each pair of the roots.paladin8noreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-20233577814105448082005-12-10T18:51:58.000-08:002005-12-10T18:51:58.000-08:00[...] We remember back here we used the one and on...[...] We remember back here we used the one and only Vieta’s Formulas, and we can do so again. [...]Mathematical Food for Thoughthttp://wangsblog.com/jeffrey/?p=29noreply@blogger.com