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A199266 Decimal expansion of x>0 satisfying 2*x^2+x*cos(x)=2.

%I A199266 #8 Feb 07 2025 16:44:05
%S A199266 8,4,8,2,4,9,6,4,9,0,6,6,0,3,3,5,6,4,4,9,3,0,0,1,6,7,1,3,6,5,3,6,0,1,
%T A199266 0,5,1,5,8,7,0,8,7,3,5,3,8,3,3,5,2,5,3,4,6,7,8,2,7,4,0,3,0,2,5,6,9,7,
%U A199266 0,7,8,0,7,5,7,1,7,7,8,1,7,4,4,8,9,5,2,7,7,9,5,8,5,6,5,4,8,8,6
%N A199266 Decimal expansion of x>0 satisfying 2*x^2+x*cos(x)=2.
%C A199266 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199266 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199266 negative: -1.11586547417780092002590535253585579273...
%e A199266 positive:  0.84824964906603356449300167136536010515870...
%t A199266 a = 2; b = 1; c = 2;
%t A199266 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199266 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199266 r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t A199266 RealDigits[r]   (* A199265 *)
%t A199266 r = x /. FindRoot[f[x] == g[x], {x, .84, .85}, WorkingPrecision -> 110]
%t A199266 RealDigits[r]   (* A199266 *)
%Y A199266 Cf. A199170.
%K A199266 nonn,cons
%O A199266 0,1
%A A199266 _Clark Kimberling_, Nov 04 2011