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A198996 Decimal expansion of x>0 satisfying 4*x^2-3*cos(x)=1.

%I A198996 #8 Feb 07 2025 19:43:51
%S A198996 8,5,9,8,8,1,1,7,5,2,3,2,0,2,6,4,4,9,5,7,8,0,4,6,0,5,2,6,3,6,4,2,8,3,
%T A198996 4,2,2,1,5,5,5,9,0,9,1,0,5,3,6,9,7,1,3,2,9,2,3,5,9,7,3,9,4,9,5,1,6,3,
%U A198996 6,5,7,4,4,5,9,1,7,1,5,4,0,9,1,1,7,9,5,3,2,8,5,8,5,3,5,4,7,3,9
%N A198996 Decimal expansion of x>0 satisfying 4*x^2-3*cos(x)=1.
%C A198996 See A198755 for a guide to related sequences. The Mathematica program includes a graph.
%H A198996 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A198996 0.85988117523202644957804605263642834221555...
%t A198996 a = 4; b = -3; c = 1;
%t A198996 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
%t A198996 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A198996 r = x /. FindRoot[f[x] == g[x], {x, .85, .86}, WorkingPrecision -> 110]
%t A198996 RealDigits[r] (* A198996 *)
%Y A198996 Cf. A198755.
%K A198996 nonn,cons
%O A198996 0,1
%A A198996 _Clark Kimberling_, Nov 01 2011