Find all real x satisfying this equation:

√(5+√(5-√(5+√(5-√(5+x))))) = x

Prove that there are no others.

(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