AoPS Forum - Algebra Pre-Olympiad Marathon • Art of Problem Solving.pdf

11/11/13AoPS Forum - Algebra Pre-Olympiad Marathon • Art of Problem Solving Algebra Pre-Olympiad Marathon Page 7 of 11 [ 212 posts ] Go to page Previous 1 ... 4, 5, 6, 7, 8, 9, 10, 11 Next Author admin25 Message Apr 27, 2012, 6:24 pm • # 121 solution new problem Introduction to Algebra A complete Algebra I course, with many additional topics from Algebra II. Over 1000 problems! Great for MATHC OUNTS and AMC preparation. Posts: 578 Blog: View Blog _________________ I am not an actual admin. There's been some confusion about this, so don't ask me to unban you. Please. "Laziness is nothing more than the act of resting before you get tired." ~Anonymous pr0likethis solution From squaring (1): Apr 27, 2012, 9:18 pm • # 122 Beast Academy The first books in our new elementary school math curriculum are now available! Posts: 785 Call this (4) From squaring (2): Call this (5) From squaring (4): Call this (6) Using (1), (4), and (6), we can construct a cubic with roots Using rational roots theorem and synthetic division (Or another method that pleases you), we see is a solution The solutions to So we find that are are all permutations of New problem _________________ "Math is not about following directions, it's about making new directions" -Lockhart GillesE Posts: 2 Location: Near 1+1i+1j+1l Apr 28, 2012, 5:34 am • # 123 solution Hidden Text www.artofproblemsolving.com/Forum/viewtopic.php?f=151&t=411040&start=120 1/6 new problem: new _________________ Noli turbare circulos meos (Archimedes of Syracus) GillesE Posts: 2 Location: Near 1+1i+1j+1l Apr 29.artofproblemsolving. 12:18 pm • # 124 Sorry. 2012.11/11/13 1+1i+1j+1l AoPS Forum .Algebra Pre-Olympiad Marathon • Art of Problem Solving We have: Furthermore: (1) (2) (3) And so: (4) (5) Where and Adding (4) and (5) yields: Substituting back yields: Therefor the answer is .com/Forum/viewtopic. So I propose a different problem: new problem _________________ Noli turbare circulos meos (Archimedes of Syracus) www.php?f=151&t=411040&start=120 2/6 . I just resolved the problem and I don't think it's an entirely algebraic problem. 8:33 pm • # 125 be a divisor of . So. If Posts: 6956 Location: Bradenton. Observe that for any . 2012. . is a divisor too. FL Blog: View Blog are the roots of .e.11/11/13 Carolstar9 Let AoPS Forum . 6:22 am • # 129 solution new problem Virgil Nicula May 04. 2012. and G. 11:44 am • # 126 @Carolstar9: A new problem perhaps? Carolstar9 May 03. Eliminate between the relations . So others. 2012. 11:54 am • # 130 Quote: PP.artofproblemsolving. feel free to post one. we have and www. and obtain i.M be Let the number of divisors be Posts: 1008 Location: Why don't you guess? So So So gstream Posts: 48 May 02. 2012.Algebra Pre-Olympiad Marathon • Art of Problem Solving Apr 29. the equation Observe that Proof 2. 2012. Posts: 1008 Location: Why don't you guess? Faustus New Problem _________________ Posts: 1219 Location: north carolina May 03. 3:00 am • # 127 I don't have any suitable problem right now. with the roots . 2012.com/Forum/viewtopic.php?f=151&t=411040&start=120 3/6 . 4:45 am • # 128 What is mind? Doesn't matter What is matter? Never mind gstream Posts: 48 May 03. then compute Proof 1. 2012. after having solved this simple problem. Find all the real values of in terms of such that May 07. gstream Posts: 48 May 07.Algebra Pre-Olympiad Marathon • Art of Problem Solving we have . 11:17 am • # 131 Is there nobody who is willing to solve my problem? Should I post the solution? swkratis Posts: 37 May 07.php?f=151&t=411040&start=120 Posts: 1821 4/6 . But remember.com/Forum/viewtopic. 2012. in this case . where . Observe that Posts: 6956 Location: Bradenton. 11:23 pm • # 136 www. But I have to say that my problem is indeed not the most difficult I could imagine Virgil Nicula PP. In conclusion. gstream Posts: 48 May 07. so not so difficult. and Equation with roots is .artofproblemsolving. 2012. In conclusion. 2012. 2:23 pm • # 133 You are free to post a new one. Observe that for any AoPS Forum . narto928 Posts: 132 Location: Dead May 16. Appear two case : in this case . 2 thank s . Proof. 2012. 1:18 pm • # 132 I think that it is very easy for this marathon. FL Blog: View Blog and and . 10:20 pm • # 135 Solve the equation in terms of .11/11/13 Proof 2. . 5:05 pm • # 134 . it's only pre-olympiad stuff. 2012. youarebad My Solution New Problem May 16. artofproblemsolving. Faustus. Faustus in the problem? Jun 08. please let me know and i will change it.com/markokarbevski feel free to add me Please rate my posts(if they are solutions or tips) and if you wish.My facebook: http://www.facebook. New Problem Peace. 6:09 am • # 140 I think the correct recursion is Quick Reply Tip: Use the full editor for advanced tags and attachments.Algebra Pre-Olympiad Marathon • Art of Problem Solving Faustus Take the smallest no. 2:01 am • # 139 Posts: 1219 Location: north carolina _________________ What is mind? Doesn't matter What is matter? Never mind abhishek_sinha Posts: 18 Location: IISc. please send constructive criticism. . Maths rookie.php?f=151&t=411040&start=120 5/6 . 2012. Bangalore Jul 20. Now take 's such that Thus. Submit Full Editor www. May 17. _________________ What is mind? Doesn't matter What is matter? Never mind Markomak1 solution new problem-Sequence May 17. Posts: 1219 Location: north carolina . 6:15 am • # 138 In case the second problem is not suitable for this section. 12:18 am • # 137 times. Sumatera Barat Blog: View Blog AoPS Forum . 2012. 2012.com/Forum/viewtopic. 2012. Thank you! Faustus What is Peace. Mode is . thanks! Posts: 512 Location: Skopje _________________ Marko Karbevski(18).11/11/13 Posts: 1821 Location: Padang Panjang. artofproblemsolving. 9. 6..php?f=151&t=411040&start=120 6/6 . 10.com/Forum/viewtopic. All R ights R e se rve d. 7.11/11/13 Display posts from previous: AoPS Forum .8 hours [ DST ] Share: Moderator: Pre-Olympiad Moderators Page 7 of 11 [ 212 posts ] Go to page Previous 1 . 11 Next Login Username: Password: Log me on automatically each visit Login You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum © C opyright 2013 AoPS Incorporate d. C ontact Us • Privacy • Te rm s & C onditions www.. 8. 4. 5.Algebra Pre-Olympiad Marathon • Art of Problem Solving All posts Sort by Post time Ascending Go Previous topic | Next topic Community » Mathematics » High School Pre-Olympiad (Ages 14+) All times are UTC .