A199181 Decimal expansion of x>0 satisfying x^2+2*x*cos(x)=3.

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

Offset: 1

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: -1.6524280450417421424058918662580123...
positive:  2.980645279438536834594908905579032175...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199170.

Programs

Mathematica

a = 1; b = 2; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199180 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.98, 2.99}, WorkingPrecision -> 110]
RealDigits[r]  (* A199181 *)