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A199281 Decimal expansion of x<0 satisfying 3*x^2+x*cos(x)=2.

%I A199281 #8 Feb 07 2025 16:44:05
%S A199281 9,2,3,2,0,7,9,6,7,0,2,2,2,7,2,9,1,8,0,8,5,3,7,0,5,6,2,9,4,6,3,7,2,1,
%T A199281 7,0,1,6,4,4,8,2,0,9,3,2,9,4,4,3,1,7,0,9,0,4,3,6,2,4,2,7,9,0,1,9,7,8,
%U A199281 8,8,9,4,8,0,1,9,7,0,6,4,8,4,7,0,2,7,4,3,6,3,2,1,4,8,8,1,7,8,8
%N A199281 Decimal expansion of x<0 satisfying 3*x^2+x*cos(x)=2.
%C A199281 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199281 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199281 negative: -0.923207967022272918085370562946372...
%e A199281 positive:  0.6988053514945826378907251192096740...
%t A199281 a = 3; b = 1; c = 2;
%t A199281 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199281 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A199281 r = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]
%t A199281 RealDigits[r]     (* A199281 *)
%t A199281 r = x /. FindRoot[f[x] == g[x], {x, .69, .70}, WorkingPrecision -> 110]
%t A199281 RealDigits[r]     (* A199282 *)
%Y A199281 Cf. A199170.
%K A199281 nonn,cons
%O A199281 0,1
%A A199281 _Clark Kimberling_, Nov 05 2011