A197812 Decimal expansion of x>0 having x^2+x=3*cos(x).

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

Offset: 0

Author

Clark Kimberling, Oct 20 2011

Keywords

• nonn
• cons

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			negative: -1.389437452704828389291498251429189255963...
positive: 0.9297344303618125096887004946976108824038...
		

Crossrefs

Cf. A197737.

Programs

Mathematica

a = 1; b = 1; c = 3;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -2, 1.5}]
r1 = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]
RealDigits[r1] (* A197811 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .92, .93}, WorkingPrecision -> 110]
RealDigits[r2] (* A197812 *)