(In reply to
another form of the answer by Larry)
Repeatedly squaring and taking care of the 5's gives
x = (5-((5-(x²-5)²)²-5)²)² - 5
Putting (1858)^1/8 into the RHS gives 2.562304215 (which differs in the seventh decimal place.) Raising this to the eighth power gives 1857.999223
My guess based on simpler equations like √(5-√(5+x)) = x
is that the squared out form will be a degree 32 polynomial with 31 real but extraneous roots. The root that works will likely involve a 32nd root but not as simply as n^(1/32)
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Posted by Jer
on 2012-12-18 13:59:18 |
re: another form of the answer - nope
