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        riddles >> medium >> Not AbSURDly Easy
        
(Message started by: ThudanBlunder on Dec 22nd, 2008, 11:36am)
Title: Not AbSURDly Easy
Post by ThudanBlunder on Dec 22nd, 2008, 11:36am
                                                                              2 + x                                                                                                                                                                        2 - x
Solve            ---------------               +                   --------------         =   http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2
                                     http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 + x)                                                         http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 - x)
Title: Re: Not AbSURDly Easy
Post by towr on Dec 23rd, 2008, 2:22am
[hideb]
(2 + x)/[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 + x)] + (2 - x)/[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 - x)] = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2
(2 + x)[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 + x)]/-x + (2 - x)[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 - x)]/x = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2
(2 - x)[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 - x)] - (2 + x)[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 + x)] = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 x
(2 - x)http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 - x) + (2 + x)http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 + x) - 2http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 x =  http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 x
(2 - x)http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 - x) + (2 + x)http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 + x) =  3http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 x
(2 - x)http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 - x) =  3 http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 x - (2 + x)http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 + x)
(2 - x)3 = 18 x2 + (2 + x)3 - 6 http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 x(2 + x)http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 + x)
18 x2 + (2 + x)3 - (2 - x)3 = 6 http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 x(2 + x)http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 + x)
(18 x2 + (2 + x)3 - (2 - x)3)2 = 72 x2(2 + x)3
4x2(x2 + 9x + 12)2 = 72 x2(2 + x)3
(x2 + 9x + 12)2 = 18(2 + x)3
x2 (x2 - 3) = 0
x = 0 v x = +/- http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3

x=0:
2/[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2] + (2)/[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2] = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 => division by 0.

x=-http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3:
(2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3)/[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3)] + (2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3)/[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3)] = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2
(2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3)/[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 + (http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif6-http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2)/2] + (2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3)/[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 - (http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif6+http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2)/2] = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2
-5 http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 => false (duh!)

x=http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3:
(2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3)/[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3)] + (2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3)/[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif(2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3)] = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2
(2 + http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3)/[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 + (http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif6+http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2)/2] + (2 - http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3)/[http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 - (http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif6-http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2)/2] = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2
http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2

==>

x = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif3
[/hideb]
Title: Re: Not AbSURDly Easy
Post by Barukh on Dec 24th, 2008, 4:48am
Hmm... I wonder if the following substitution [hide]x = 2cos(y)[/hide] may lead to a more succinct solution?

:-/


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