OFFSET
1,2
COMMENTS
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.
FORMULA
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]
EXAMPLE
1.28378166586...
MATHEMATICA
RealDigits[x /. FindRoot[x^4 + x - 4, {x, 1}, WorkingPrecision -> 100], 10, 90][[1]] (* Amiram Eldar, Sep 03 2020 *)
PROG
(PARI) solve(n=0, 2, n^4+n-4)
(PARI) polroots(n^4+n-4)[2]
(PARI) polrootsreal(x^4+x-4)[2] \\ Charles R Greathouse IV, Oct 27 2023
(MATLAB) format long; solve('x^4+x-4=0'); ans(3), (eval(ans))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Michal Paulovic, Sep 01 2020
STATUS
approved