A337570 Decimal expansion of the real positive solution to x^4 = 4-x.

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

Offset: 1

Author

Michal Paulovic, Sep 01 2020

Keywords

• nonn
• cons

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.

Examples

			1.28378166586...
		

Links

• Index entries for algebraic numbers, degree 4

Crossrefs

Cf. A337571.

Programs

MATLAB

format long; solve('x^4+x-4=0'); ans(3), (eval(ans))

Mathematica

RealDigits[x /. FindRoot[x^4 + x - 4, {x, 1}, WorkingPrecision -> 100], 10, 90][[1]] (* Amiram Eldar, Sep 03 2020 *)

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

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]