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A199283 Decimal expansion of x<0 satisfying 3*x^2+x*cos(x)=3.

%I A199283 #9 Feb 07 2025 16:44:05
%S A199283 1,0,8,1,4,1,1,5,9,7,1,9,4,6,7,7,5,4,8,2,8,5,1,5,3,7,5,1,5,9,2,1,6,4,
%T A199283 2,7,8,8,2,0,0,2,3,6,3,6,9,7,1,5,3,4,4,8,5,9,6,8,1,5,6,9,3,7,6,7,4,4,
%U A199283 3,9,4,4,9,9,4,3,7,2,3,9,6,5,5,2,2,4,7,1,4,5,7,7,2,9,1,9,6,1,7
%N A199283 Decimal expansion of x<0 satisfying 3*x^2+x*cos(x)=3.
%C A199283 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199283 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199283 negative: -1.081411597194677548285153751592164...
%e A199283 positive:  0.901983106002417964495821536577097...
%t A199283 a = 3; b = 1; c = 3;
%t A199283 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199283 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A199283 r = x /. FindRoot[f[x] == g[x], {x, -1.1, -1.0}, WorkingPrecision -> 110]
%t A199283 RealDigits[r]     (* A199283 *)
%t A199283 r = x /. FindRoot[f[x] == g[x], {x, .9, 1}, WorkingPrecision -> 110]
%t A199283 RealDigits[r]    (* A199284 *)
%Y A199283 Cf. A199170.
%K A199283 nonn,cons
%O A199283 1,3
%A A199283 _Clark Kimberling_, Nov 05 2011