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A199274 Decimal expansion of x>0 satisfying 2*x^2+3*x*cos(x)=1.

%I A199274 #8 Feb 07 2025 16:44:05
%S A199274 2,8,9,5,0,5,4,4,8,3,8,5,8,6,7,4,1,5,5,9,2,1,7,9,4,8,3,1,9,8,9,8,2,4,
%T A199274 5,2,3,8,1,3,1,4,3,3,8,6,3,2,2,5,8,1,1,4,5,6,8,0,7,2,4,0,2,8,2,3,6,7,
%U A199274 2,1,2,5,7,1,2,9,9,1,1,0,3,1,6,6,7,0,2,8,3,6,5,7,4,5,9,6,1,4,0
%N A199274 Decimal expansion of x>0 satisfying 2*x^2+3*x*cos(x)=1.
%C A199274 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199274 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199274 negative: -1.11270716122321939210526043888351330910...
%e A199274 positive:  0.289505448385867415592179483198982452381...
%t A199274 a = 2; b = 3; c = 1;
%t A199274 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199274 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A199274 r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t A199274 RealDigits[r]    (* A199273 *)
%t A199274 r = x /. FindRoot[f[x] == g[x], {x, .28, .29}, WorkingPrecision -> 110]
%t A199274 RealDigits[r]    (* A199274 *)
%Y A199274 Cf. A199170.
%K A199274 nonn,cons
%O A199274 0,1
%A A199274 _Clark Kimberling_, Nov 04 2011