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A199286 Decimal expansion of x>0 satisfying 3*x^2+2*x*cos(x)=1.

%I A199286 #8 Feb 07 2025 16:44:05
%S A199286 3,4,3,2,7,2,8,1,9,6,2,7,0,0,0,4,2,6,4,7,8,6,9,7,0,2,7,5,0,9,7,0,2,6,
%T A199286 9,5,3,1,9,3,1,1,0,4,5,2,6,1,0,3,2,9,0,4,8,1,3,0,3,7,5,1,5,8,9,1,1,2,
%U A199286 9,5,4,7,8,8,9,4,9,5,1,5,5,3,0,5,6,4,0,7,8,5,8,3,0,2,6,1,1,3,0
%N A199286 Decimal expansion of x>0 satisfying 3*x^2+2*x*cos(x)=1.
%C A199286 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199286 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199286 negative: -0.840914700055474492704399020053615852...
%e A199286 positive:  0.3432728196270004264786970275097026953...
%t A199286 a = 3; b = 2; c = 1;
%t A199286 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199286 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199286 r = x /. FindRoot[f[x] == g[x], {x, -.85, -.84}, WorkingPrecision -> 110]
%t A199286 RealDigits[r]    (* A199285 *)
%t A199286 r = x /. FindRoot[f[x] == g[x], {x, .34, .35}, WorkingPrecision -> 110]
%t A199286 RealDigits[r]    (* A199286 *)
%Y A199286 Cf. A199170.
%K A199286 nonn,cons
%O A199286 0,1
%A A199286 _Clark Kimberling_, Nov 05 2011