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You are not logged in. #26 20060308 00:32:57
Re: *** Problems***5 #27 20060308 03:33:47
Re: *** Problemsashwil, I shall post the solution to ***3 tomorrow. I was occupied with the other topics today. (Particularly, my post on quotes of mathematicians in 'Members only'). Character is who you are when no one is looking. #28 20060308 05:53:10
Re: *** ProblemsI'll settle for my reasoning being good. When you don't spend your time actually doing mathematical proofs, you do forget the notation, the methodology and the formulae, but reasoning powers can still get you a long way! #29 20060308 06:24:15
Re: *** Problems***5 Thus, it becomes apparent we must show: Where If x < 1, then Since all of the negative powers of x must be greater than or equal to 1. The same reasoning goes for x > 2, But I can't seem to get the numbers in between 1 and 2. Edit: How's this for an argument? The graph is continuous, above, and never intersects with 94 for all positive values x less than 2. Thus, it must always be greater there. Last edited by Ricky (20060308 06:36:19) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #30 20060308 06:36:52
Re: *** ProblemsLogaritms? IPBLE: Increasing Performance By Lowering Expectations. #31 20060308 06:47:38
Re: *** ProblemsCan someone do this: IPBLE: Increasing Performance By Lowering Expectations. #32 20060308 07:00:57
Re: *** ProblemsWell done, Ricky! IPBLE: Increasing Performance By Lowering Expectations. #33 20060308 07:21:51
Re: *** Problems***5 IPBLE: Increasing Performance By Lowering Expectations. #34 20060308 07:23:24
Re: *** ProblemsLet IPBLE: Increasing Performance By Lowering Expectations. #35 20060308 07:25:00
Re: *** ProblemsHere's a plot: Last edited by krassi_holmz (20060308 07:25:44) IPBLE: Increasing Performance By Lowering Expectations. #36 20060308 07:28:51
Re: *** ProblemsWe need to find the minimum for x>0 (actually we don't need the other side because a,b,c are positive). Last edited by krassi_holmz (20060308 07:29:21) IPBLE: Increasing Performance By Lowering Expectations. #37 20060308 07:40:39
Re: *** ProblemsThe main thing is that f'(x) is factorizible: So clearly the roots of f'(x)=0 are x=1 or x=4/3. leaving 1. So f(x) has minimum at x=4/3!!! And here's where the stinky comes: f(4/3)=823543/6912=119.147... So for ALL x>0 f(x)>=119.147...!!! But then f(a)f(b)f(c)>=119.147...^3=558545864083284007 / 330225942528=1691405.16... But the main question was to prove that f(a)f(b)f(c)>=823543 {/*this is 7^7*/} And ricky an I got that: f(a)f(b)f(c)>=1691405.16 and the minimum is at {a,b,c}={4/3,4/3,4/3}. Am I wrong? IPBLE: Increasing Performance By Lowering Expectations. #38 20060308 18:17:19
Re: *** ProblemsGanesh, please reply. IPBLE: Increasing Performance By Lowering Expectations. #39 20060308 18:25:37
Re: *** ProblemsSure, krassi_holmz. The problem is being approached in a much different way than I expected. The solution I had to the problem didn't involve differentiation and maximum/minimum. I shall wait for other responses, particularly from mathsyperson/irspow/John. Please wait for the solution for a day more. Character is who you are when no one is looking. #40 20060308 18:43:40
Re: *** ProblemsBut I'm confused about this: f(a)f(b)f(c)>=7^7 Last edited by krassi_holmz (20060309 05:02:48) IPBLE: Increasing Performance By Lowering Expectations. #41 20060308 18:47:42
Re: *** Problemssomewhere... IPBLE: Increasing Performance By Lowering Expectations. #42 20060309 02:34:22
Re: *** ProblemsSolution to ***3 or 5e (on simplification). Since we started the series as 3² /1! + 5² /3! + 7² /5! +.........., 1 should be added to the sum. Hence the sum to infinity is 1+5e. Character is who you are when no one is looking. #43 20060309 02:55:35
Re: *** ProblemsMany thanks. I had forgotten the technique of considering the nth term. All now clear. #44 20060309 15:10:32
Re: *** Problems***6 Character is who you are when no one is looking. #45 20060309 18:14:17
Re: *** Problems***6 beautiful! so: Let reduce the left side: Last edited by krassi_holmz (20060309 18:23:57) IPBLE: Increasing Performance By Lowering Expectations. #47 20060310 18:22:51
Re: *** Problems***7 and if z be a complex number such that then prove that z  7 9i = 3√2. Character is who you are when no one is looking. #48 20060311 16:43:21
Re: *** Problems***8 Character is who you are when no one is looking. #49 20060312 17:11:47
Re: *** Problems***9 Character is who you are when no one is looking. #50 20060313 01:23:36
Re: *** Problems***10 Character is who you are when no one is looking. 