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%I #8 Aug 09 2021 07:41:05
%S 3,6,9,2,3,4,7,7,7,3,9,2,7,9,8,9,8,6,0,1,8,2,8,4,7,7,0,6,2,9,9,4,0,1,
%T 0,4,9,8,7,2,7,9,3,8,2,1,9,3,0,3,1,4,4,1,9,0,0,1,4,4,4,4,4,2,3,9,5,3,
%U 1,0,9,9,2,4,3,7,1,6,5,6,8,5,9,2,7,2,9,3,0,3,1,0,2,6,3,1,9,6,3
%N Decimal expansion of greatest x having x^2-3x=-3*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: 0.89291071141777527373996831831704569...
%e greatest x: 3.69234777392798986018284770629940...
%t a = 1; b = -3; c = -3;
%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, -1, 4}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, 0.89, 0.90}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A198142 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, 3.6, 3.7}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A198143 *)
%Y Cf. A197737.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 21 2011
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