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A198937 Decimal expansion of x>0 satisfying 3*x^2-4*cos(x)=-2.

%I A198937 #9 Feb 07 2025 17:56:51
%S A198937 6,3,6,7,1,4,1,7,4,1,0,4,2,3,6,7,1,3,8,6,4,2,0,9,0,7,1,7,5,8,4,5,2,8,
%T A198937 7,9,7,3,2,4,8,8,3,8,5,7,7,4,3,7,3,2,8,8,6,1,3,6,7,7,7,3,5,7,4,8,1,0,
%U A198937 5,8,0,0,4,1,7,2,0,1,7,4,8,6,5,1,7,1,9,7,2,6,5,6,7,5,6,4,5,9,8
%N A198937 Decimal expansion of x>0 satisfying 3*x^2-4*cos(x)=-2.
%C A198937 See A198755 for a guide to related sequences. The Mathematica program includes a graph.
%H A198937 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A198937 0.6367141741042367138642090717584528797324883...
%t A198937 a = 3; b = -4; c = -2;
%t A198937 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
%t A198937 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A198937 r = x /. FindRoot[f[x] == g[x], {x, .63, .64}, WorkingPrecision -> 110]
%t A198937 RealDigits[r] (* A198937 *)
%Y A198937 Cf. A198755.
%K A198937 nonn,cons
%O A198937 0,1
%A A198937 _Clark Kimberling_, Nov 01 2011