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A198989 Decimal expansion of x>0 satisfying 4*x^2-cos(x)=3.

%I A198989 #8 Feb 07 2025 19:45:33
%S A198989 9,4,6,6,2,8,5,1,6,7,6,8,7,8,1,1,7,4,9,2,2,2,5,4,2,2,9,6,4,8,4,8,7,2,
%T A198989 4,7,0,4,1,1,9,9,9,4,8,3,6,3,0,0,8,7,7,5,0,0,2,2,0,5,3,5,4,6,6,5,3,1,
%U A198989 1,5,9,3,3,3,6,2,9,5,6,7,3,7,3,6,0,4,1,7,4,0,0,0,7,0,0,3,9,0,2
%N A198989 Decimal expansion of x>0 satisfying 4*x^2-cos(x)=3.
%C A198989 See A198755 for a guide to related sequences. The Mathematica program includes a graph.
%H A198989 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A198989 0.9466285167687811749222542296484872470411999...
%t A198989 a = 4; b = -1; c = 3;
%t A198989 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
%t A198989 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A198989 r = x /. FindRoot[f[x] == g[x], {x, .94, .95}, WorkingPrecision -> 110]
%t A198989 RealDigits[r] (* A198989 *)
%Y A198989 Cf. A198755.
%K A198989 nonn,cons
%O A198989 0,1
%A A198989 _Clark Kimberling_, Nov 01 2011