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A337570
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Decimal expansion of the real positive solution to x^4 = 4-x.
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1
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1, 2, 8, 3, 7, 8, 1, 6, 6, 5, 8, 6, 3, 5, 3, 8, 2, 0, 8, 3, 0, 5, 2, 6, 4, 3, 2, 9, 5, 7, 0, 4, 7, 2, 1, 5, 0, 8, 7, 6, 4, 6, 2, 8, 1, 6, 2, 3, 9, 7, 0, 2, 0, 1, 2, 9, 7, 2, 8, 5, 7, 3, 2, 9, 8, 7, 9, 3, 6, 0, 5, 0, 2, 4, 0, 2, 3, 7, 4, 2, 7, 6, 1, 7, 1, 8, 4, 7, 8, 3, 5, 8, 0, 1, 2, 2, 9
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OFFSET
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1,2
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COMMENTS
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x = (4 - (4 - (4 - ... )^(1/4))^(1/4))^(1/4).
The negative value (-1.2837816658...) is the real negative solution to x^4 = x+4.
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LINKS
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FORMULA
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Equals sqrt(sqrt(1/s) - s/16) - sqrt(s/16) where s = (sqrt(16804864/27) + 32)^(1/3) - (sqrt(16804864/27) - 32)^(1/3). [Simplified by Michal Paulovic, Jun 22 2021]
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EXAMPLE
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1.28378166586...
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MATHEMATICA
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RealDigits[x /. FindRoot[x^4 + x - 4, {x, 1}, WorkingPrecision -> 100], 10, 90][[1]] (* Amiram Eldar, Sep 03 2020 *)
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PROG
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(PARI) solve(n=0, 2, n^4+n-4)
(PARI) polroots(n^4+n-4)[2]
(MATLAB) format long; solve('x^4+x-4=0'); ans(3), (eval(ans))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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