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A199186 Decimal expansion of x<0 satisfying x^2+3*x*cos(x)=3.

%I A199186 #8 Feb 07 2025 16:44:05
%S A199186 1,6,3,6,4,4,3,5,5,1,9,5,5,0,4,1,4,2,2,0,6,7,5,9,3,0,3,1,1,8,7,1,2,8,
%T A199186 2,4,5,5,9,3,6,5,4,1,7,1,8,5,9,0,2,6,8,4,2,5,3,3,4,8,5,5,7,2,4,9,6,0,
%U A199186 1,4,7,7,1,1,7,8,8,6,4,9,0,3,3,9,7,9,7,6,2,3,7,9,1,6,2,1,2,7,2
%N A199186 Decimal expansion of x<0 satisfying x^2+3*x*cos(x)=3.
%C A199186 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199186 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199186 negative: -1.6364435519550414220675930311871282455...
%e A199186 positive:  3.56968633396230393049792896687800143343...
%t A199186 a = 1; b = 3; c = 3;
%t A199186 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199186 Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
%t A199186 Plot[{f[x], g[x]}, {x, 0, 2}, {AxesOrigin -> {0, 0}}]
%t A199186 r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]
%t A199186 RealDigits[r]  (* A199186 *)
%t A199186 r = x /. FindRoot[f[x] == g[x], {x, 3.56, 3.57}, WorkingPrecision -> 110]
%t A199186 RealDigits[r]  (*  A199187 *)
%Y A199186 Cf. A199170.
%K A199186 nonn,cons
%O A199186 1,2
%A A199186 _Clark Kimberling_, Nov 04 2011