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wu :: forums    riddles    medium (Moderators: william wu, Grimbal, Icarus, ThudnBlunder, towr, Eigenray, SMQ)    Not AbSURDly Easy « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Not AbSURDly Easy  (Read 680 times) ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Not AbSURDly Easy   « on: Dec 22nd, 2008, 11:36am » Quote Modify              2 + x                            2 - x Solve  ---------------     +    --------------    =   2         2 + (2 + x)            2 - (2 - x) IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Not AbSURDly Easy   « Reply #1 on: Dec 23rd, 2008, 2:22am » Quote Modify hidden: (2 + x)/[2 + (2 + x)] + (2 - x)/[2 - (2 - x)] = 2 (2 + x)[2 - (2 + x)]/-x + (2 - x)[2 + (2 - x)]/x = 2 (2 - x)[2 + (2 - x)] - (2 + x)[2 - (2 + x)] = 2 x (2 - x)(2 - x) + (2 + x)(2 + x) - 22 x =  2 x (2 - x)(2 - x) + (2 + x)(2 + x) =  32 x (2 - x)(2 - x) =  3 2 x - (2 + x)(2 + x)   (2 - x)3 = 18 x2 + (2 + x)3 - 6 2 x(2 + x)(2 + x)   18 x2 + (2 + x)3 - (2 - x)3 = 6 2 x(2 + x)(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 = +/- 3   x=0: 2/[2 + 2] + (2)/[2 - 2] = 2 => division by 0.   x=-3: (2 - 3)/[2 + (2 - 3)] + (2 + 3)/[2 - (2 + 3)] = 2 (2 - 3)/[2 + (6-2)/2] + (2 + 3)/[2 - (6+2)/2] = 2 -5 2 = 2 => false (duh!)   x=3:   (2 + 3)/[2 + (2 + 3)] + (2 - 3)/[2 - (2 - 3)] = 2 (2 + 3)/[2 + (6+2)/2] + (2 - 3)/[2 - (6-2)/2] = 2 2 = 2   ==>   x = 3 IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Barukh Uberpuzzler     Gender: Posts: 2276 Re: Not AbSURDly Easy   « Reply #2 on: Dec 24th, 2008, 4:48am » Quote Modify Hmm... I wonder if the following substitution x = 2cos(y) may lead to a more succinct solution?     IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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