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Five Fives Fancy Formula (Posted on 2012-12-17) Difficulty: 3 of 5
Find all real x satisfying this equation:

√(5+√(5-√(5+√(5-√(5+x))))) = x

Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
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re(2): another form of the answer - nope Comment 4 of 4 |
(In reply to re: another form of the answer - nope by Jer)

(5-((5-(x^2-5)^2)^2-5)^2)^2 - 5 - x into polynomial form:
x32-80x30+2960x28-67200x26+1047180x24-11870800x22+101215600x20-661880000x18+3353680140x16-13207205600x14+40284095200x12-94160896000x10+165349095600x8-210897912000x6+184294024000x4-98604640000x2-x+24342240395

Which factors as: (x2-x-5) (x30+x29-74x28-69x27+2521x26+2176x25-52419x24-41539x23+743546x22+535851x21-7617219x20-4937964x19+58191541x18+33501721x17-337420574x16-169911969x15+1496665301x14+647105456x13-5076773639x12-1841246359x11+13058980646x10+3852748851x9-25013243919x8-5749499664x7+34533376341x6+5785878021x5-32445152274x4-3515762169x3+18552500461x2+973689616x-4868448079)


  Posted by Brian Smith on 2012-12-22 15:00:02
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