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

%I #5 Mar 30 2012 18:57:53

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

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

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

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

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

%e least x: -1.5399952272668390818059885802040...

%e greatest x: 0.6975345552284129937951740662521298...

%t a = 2; b = 3; c = 4;

%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, -1.54, -1.539}, WorkingPrecision -> 110]

%t RealDigits[r1](* A198134 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .79, .70}, WorkingPrecision -> 110]

%t RealDigits[r2](* A198135 *))

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 22 2011