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

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

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

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

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

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

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

%e least x: -1.53498632262030720596966252020141464...

%e greatest x: 0.593780812679159037660816455610994...

%t a = 2; b = 3; 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, -1.54, -1.53}, WorkingPrecision -> 110]

%t RealDigits[r1](* A198132 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .59, .60}, WorkingPrecision -> 110]

%t RealDigits[r2](* A198133 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 22 2011