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%I #5 Mar 30 2012 18:57:53
%S 7,6,5,7,2,6,4,4,2,9,2,0,5,4,0,7,1,7,4,8,3,1,0,1,0,4,9,2,3,9,4,4,9,9,
%T 3,8,2,5,9,3,8,8,0,0,4,2,0,4,9,6,3,7,0,7,0,8,5,2,1,5,1,7,2,8,8,4,5,8,
%U 6,9,4,9,7,5,8,1,7,4,9,7,9,4,2,2,8,3,9,2,5,1,1,7,8,8,9,2,8,8,8
%N Decimal expansion of greatest x having x^2+3x=4*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: -2.072191302711809327379682290027003...
%e greatest x: 0.7657264429205407174831010492394...
%t a = 1; b = 3; c = 4;
%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, -3, 1}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, -2.1, -2.9}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A198108 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, .76, .77}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A198109 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 21 2011