A199274 Decimal expansion of x>0 satisfying 2*x^2+3*x*cos(x)=1.

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

Offset: 0

Author

Clark Kimberling, Nov 04 2011

Keywords

• nonn
• cons

Comments

See A199170 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			negative: -1.11270716122321939210526043888351330910...
positive:  0.289505448385867415592179483198982452381...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199170.

Programs

Mathematica

a = 2; b = 3; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
RealDigits[r]    (* A199273 *)
r = x /. FindRoot[f[x] == g[x], {x, .28, .29}, WorkingPrecision -> 110]
RealDigits[r]    (* A199274 *)