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A199268 Decimal expansion of x > 0 satisfying 2*x^2 + x*cos(x) = 3.

%I A199268 #13 Feb 07 2025 16:44:05
%S A199268 1,1,2,0,8,2,7,8,9,9,0,7,2,4,6,4,1,0,5,0,1,0,8,0,2,6,5,5,1,2,3,8,2,4,
%T A199268 4,1,4,8,4,1,5,4,0,8,0,2,6,3,1,7,7,8,5,0,7,9,0,8,7,2,0,2,4,4,4,0,8,1,
%U A199268 6,1,3,3,0,6,8,0,5,0,0,7,0,6,7,6,8,3,8,6,5,7,0,5,7,9,1,6,6,0,3
%N A199268 Decimal expansion of x > 0 satisfying 2*x^2 + x*cos(x) = 3.
%C A199268 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199268 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199268 negative: -1.29477176551027054190068103147021856144266...
%e A199268 positive:  1.120827899072464105010802655123824414841540...
%t A199268 a = 2; b = 1; c = 3;
%t A199268 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199268 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199268 r = x /. FindRoot[f[x] == g[x], {x, -1.3, -1.2}, WorkingPrecision -> 110]
%t A199268 RealDigits[r]    (* A199267 *)
%t A199268 r = x /. FindRoot[f[x] == g[x], {x, 1.12, 1.13}, WorkingPrecision -> 110]
%t A199268 RealDigits[r]    (* A199268 *)
%Y A199268 Cf. A199170, A199267.
%K A199268 nonn,cons
%O A199268 1,3
%A A199268 _Clark Kimberling_, Nov 04 2011
%E A199268 a(89) onwards corrected by _Georg Fischer_, Aug 03 2021