A329998 Decimal expansion of the solution of 1/sqrt(x-1) + 1/sqrt(x+1) = 1.

4, 1, 8, 1, 1, 2, 5, 4, 4, 5, 2, 9, 2, 6, 7, 4, 3, 0, 0, 5, 4, 4, 5, 8, 2, 5, 6, 0, 2, 1, 1, 8, 9, 8, 0, 8, 0, 6, 0, 8, 5, 6, 6, 3, 6, 3, 0, 8, 9, 7, 2, 1, 1, 5, 2, 5, 6, 7, 8, 2, 0, 7, 6, 9, 6, 6, 9, 9, 7, 5, 2, 6, 2, 4, 4, 2, 6, 9, 6, 2, 6, 1, 3, 8, 4, 9

Offset

1,1

Links

Table of n, a(n) for n=1..86.

Index entries for algebraic numbers, degree 4.

Formula

x^4 - 4 x^3 - 2 x^2 + 4 x + 5 = 0.

Example

4.1811254452926743005445825602118...

Mathematica

r = x /. FindRoot[1/Sqrt[x - 1] + 1/Sqrt[x + 1] == 1, {x, 2, 10}, WorkingPrecision -> 210]
RealDigits[r][[1]] (* A329998 *)
Plot[1/Sqrt[x - 1] + 1/Sqrt[x + 1] - 1, {x, 1, 6}]

Prog

(PARI) solve(x=4, 5, 1/sqrt(x-1) + 1/sqrt(x+1)-1) \\ Charles R Greathouse IV, May 18 2026
(PARI) polrootsreal(x^4 - 4*x^3 - 2*x^2 + 4*x + 5)[2] \\ Charles R Greathouse IV, May 18 2026

Crossrefs

Cf. A329999, A330000.

Sequence in context: A262361 A294791 A084884 * A143320 A384999 A089146

Adjacent sequences: A329995 A329996 A329997 * A329999 A330000 A330001

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jan 03 2020

Status

approved