%I #5 Mar 30 2012 18:57:54

%S 4,8,6,0,0,4,4,3,5,9,9,2,2,9,3,0,4,0,8,1,6,1,9,8,9,8,1,5,0,3,5,7,8,5,

%T 6,4,6,9,2,1,1,0,8,7,9,7,3,0,9,4,7,7,4,2,5,5,3,7,9,8,3,9,2,2,9,1,8,0,

%U 2,6,8,1,9,8,3,7,6,9,9,0,9,0,6,2,7,7,5,3,7,1,6,2,9,0,0,4,5,7,7

%N Decimal expansion of greatest x having 3*x^2+4x=3*cos(x).

%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.

%e least x: -1.4308334207177285425665439336391388599...

%e greatest x: 0.48600443599229304081619898150357856...

%t a = 3; b = 4; c = 3;

%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]

%t Plot[{f[x], g[x]}, {x, -2, 1}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, -1.5, -1.4}, WorkingPrecision -> 110]

%t RealDigits[r1](* A198240 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .48, .49}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198241 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 23 2011