Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20060227 16:13:36
Indices and SurdsIS # 1 Character is who you are when no one is looking. #2 20060227 17:13:32
Re: Indices and SurdsYo ho ho IPBLE: Increasing Performance By Lowering Expectations. #4 20060227 17:31:38
Re: Indices and SurdsOK. I'm ready with IS1. IPBLE: Increasing Performance By Lowering Expectations. #5 20060227 17:35:36
Re: Indices and SurdsSoe here is it: a^x=b^y=c^z=(ac)^(y/2); a^x=(ac)^(y/2) x=log(a,(ac)^(y/2))=y(1+loga,c)/2 z=y(1+logc,a)/2 M=1/z+1/x=2/y(1+log a,c)+2/y(1+log c,a)=2(log a,c +log c,a +2)/y(1+log a,c)(1+log c,a)= 2/y)(log a,c +log c,a +2)/(1+log a,c+log c,a+(log a,c)(log c,a))= 2/y)(log a,c +log c,a +2)/(1+log a,c+log c,a+(log a,c)(log c,a)); a^x=c =>c^(1/x)=a => (log a,c)(log c,a)=1 => M=2/y. Last edited by krassi_holmz (20060227 17:50:04) IPBLE: Increasing Performance By Lowering Expectations. #6 20060227 18:11:15
Re: Indices and SurdsThat solution is too complicated. I am unable to check whether its correct right now. There's a much simpler solution, krassi_holmz. I shall post that a little later. Character is who you are when no one is looking. #7 20060227 19:35:43
Re: Indices and SurdsHere's the simpler solution: IPBLE: Increasing Performance By Lowering Expectations. #8 20060227 19:38:10
Re: Indices and SurdsIs it clear now? IPBLE: Increasing Performance By Lowering Expectations. #9 20060227 20:29:48
Re: Indices and SurdsIn your post, I was not able to go far. Character is who you are when no one is looking. #10 20060227 20:42:02
Re: Indices and SurdsYes, my second proof is just like yours, but instead plugging (1/x) and (1/z) in the power equation, I first solve it to get integer powers: Now i'm poving that b^xz=b^2y(x+z): Last edited by krassi_holmz (20060227 21:09:00) IPBLE: Increasing Performance By Lowering Expectations. #11 20060227 21:10:20
Re: Indices and Surdsnow, won't give second q? IPBLE: Increasing Performance By Lowering Expectations. #12 20060301 15:19:16
Re: Indices and SurdsIS # 2 Character is who you are when no one is looking. #13 20060301 16:28:50
Re: Indices and Surds7+3√5 = (14+6√5) / 2 = ( 3 + √5 )² / 2 #14 20060301 16:43:27
Re: Indices and SurdsThe first row is fine but I can't get the second: Last edited by krassi_holmz (20060301 16:48:31) IPBLE: Increasing Performance By Lowering Expectations. #15 20060301 18:52:26
Re: Indices and SurdsWell done, rimi and krassi_holmz! Character is who you are when no one is looking. #16 20060301 19:26:10
Re: Indices and SurdsIPBLE: Increasing Performance By Lowering Expectations. #17 20060301 19:31:34
Re: Indices and Surdsthe first is whitout + and rimi gave correct rationalization of the denominator. IPBLE: Increasing Performance By Lowering Expectations. #18 20060302 19:59:17
Re: Indices and SurdsIS # 3 Character is who you are when no one is looking. #19 20060303 01:32:10
Re: Indices and SurdsIPBLE: Increasing Performance By Lowering Expectations. #20 20060303 01:34:45
Re: Indices and SurdsIs#3=3=3+0√5 IPBLE: Increasing Performance By Lowering Expectations. #22 20060310 02:34:26
Re: Indices and SurdsIS # 4 Character is who you are when no one is looking. #23 20060311 15:29:59
Re: Indices and SurdsIS # 5 Character is who you are when no one is looking. #24 20070322 02:53:47
Re: Indices and Surdssolution :  #25 20070322 03:44:00 