My Math Forum Eddybob's problem of the week

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 September 8th, 2013, 09:19 PM #1 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,950 Thanks: 987 Eddybob's problem of the week Here's what Wolfram has if the 10^10 is replaced by a (10^20 = a^2): http://www.wolframalpha.com/input/?i=so ... %3D0+for+x YIKES
 September 9th, 2013, 03:20 PM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Eddybob's problem of the week Weird. Where do all the decimals come from?
 September 9th, 2013, 08:06 PM #3 Senior Member   Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 Re: Eddybob's problem of the week Get the roots to 4 decimal places. I understand that the exact values are quite complicated.
September 9th, 2013, 09:15 PM   #4
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Re: Eddybob's problem of the week

Quote:
 Originally Posted by CRGreathouse Weird. Where do all the decimals come from?
Ya ain't seen nuttin' yet; go enter: x^4-(2*10^10-1)*x^3-x+10^20+10^10-1=0
here: http://www.numberempire.com/equationsolver.php

 September 10th, 2013, 01:21 PM #5 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,950 Thanks: 987 Re: Eddybob's problem of the week x^4 - (2*10^10 - 1) * x^3 - x + 10^20 + 10^10 - 1 = 0 Let k = 10^10; then we have a quadratic: k^2 + (1 - 2x^3)k + x^4 + x^3 - x - 1 = 0 2k = 2x^3 - 1 +- SQRT(4x^6 - 4x^4 - 8x^3 + 4x + 5) Ya, I know...so what!?
 September 10th, 2013, 04:23 PM #6 Senior Member   Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 Re: Eddybob's problem of the week You really know how to cheat, do you?
 September 10th, 2013, 07:53 PM #7 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,950 Thanks: 987 Re: Eddybob's problem of the week If you say so...

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