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A198941 Decimal expansion of x>0 satisfying 3*x^2-4*cos(x)=3.

%I A198941 #8 Feb 07 2025 17:57:48
%S A198941 1,2,1,1,7,9,6,4,7,4,6,7,1,9,7,7,5,7,7,4,8,1,4,0,7,2,1,2,9,1,6,5,4,8,
%T A198941 0,2,2,5,0,0,2,8,1,2,7,0,2,6,0,6,1,4,0,2,2,3,6,4,0,4,3,2,6,7,3,4,7,8,
%U A198941 2,4,5,1,0,0,7,9,1,2,0,8,9,9,5,0,6,2,7,1,8,9,8,4,2,2,7,4,2,1,8
%N A198941 Decimal expansion of x>0 satisfying 3*x^2-4*cos(x)=3.
%C A198941 See A198755 for a guide to related sequences. The Mathematica program includes a graph.
%H A198941 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A198941 1.211796474671977577481407212916548022500...
%t A198941 a = 3; b = -4; c = 3;
%t A198941 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
%t A198941 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A198941 r = x /. FindRoot[f[x] == g[x], {x, 1.21, 1.22}, WorkingPrecision -> 110]
%t A198941 RealDigits[r] (* A198941 *)
%Y A198941 Cf. A198755.
%K A198941 nonn,cons
%O A198941 1,2
%A A198941 _Clark Kimberling_, Nov 01 2011