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A199289 Decimal expansion of x<0 satisfying 3*x^2+2*x*cos(x)=3.

%I A199289 #8 Feb 07 2025 16:44:05
%S A199289 1,1,4,6,5,7,2,9,9,3,9,3,1,2,4,4,6,6,5,9,0,5,1,0,9,4,9,1,4,1,6,2,0,6,
%T A199289 5,8,2,5,9,8,6,7,6,3,1,6,6,2,9,4,2,9,0,2,9,9,1,1,9,2,6,0,6,8,6,4,4,6,
%U A199289 7,0,6,8,1,0,6,1,5,3,9,1,0,2,6,0,1,7,6,0,7,3,7,8,8,5,1,5,3,7,9
%N A199289 Decimal expansion of x<0 satisfying 3*x^2+2*x*cos(x)=3.
%C A199289 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199289 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199289 negative: -1.1465729939312446659051094914162065825...
%e A199289 positive:  0.79310716512209201308469669867166689386...
%t A199289 a = 3; b = 2; c = 3;
%t A199289 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199289 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199289 r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t A199289 RealDigits[r]    (* A199289 *)
%t A199289 r = x /. FindRoot[f[x] == g[x], {x, .79, .80}, WorkingPrecision -> 110]
%t A199289 RealDigits[r]    (* A199290 *)
%Y A199289 Cf. A199170.
%K A199289 nonn,cons
%O A199289 1,3
%A A199289 _Clark Kimberling_, Nov 05 2011