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A199292 Decimal expansion of x>0 satisfying 3*x^2+3*x*cos(x)=1.

%I A199292 #8 Feb 07 2025 16:44:05
%S A199292 2,7,0,1,5,0,2,8,9,6,3,1,8,0,3,2,5,8,0,2,0,9,7,7,8,4,6,1,2,6,9,8,6,0,
%T A199292 4,4,6,0,7,8,8,6,9,5,1,4,6,6,2,3,2,3,5,2,8,3,8,1,5,8,4,6,7,7,6,1,8,7,
%U A199292 5,8,8,2,1,3,0,7,1,2,3,6,4,2,1,7,1,3,3,4,7,2,5,8,6,4,3,8,3,1,5
%N A199292 Decimal expansion of x>0 satisfying 3*x^2+3*x*cos(x)=1.
%C A199292 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199292 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199292 negative: -0.942013171745925470278385478816333...
%e A199292 positive:  0.2701502896318032580209778461269860...
%t A199292 a = 3; b = 3; c = 1;
%t A199292 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199292 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A199292 r = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]
%t A199292 RealDigits[r]     (* A199291 *)
%t A199292 r = x /. FindRoot[f[x] == g[x], {x, .27, .28}, WorkingPrecision -> 110]
%t A199292 RealDigits[r]    (* A199292 *)
%Y A199292 Cf. A199170.
%K A199292 nonn,cons
%O A199292 0,1
%A A199292 _Clark Kimberling_, Nov 05 2011