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

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

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

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

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

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

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

%e least x: -1.303688236082731236157942349201731581...

%e greatest x: 0.68722829225254885401536676699761905...

%t a = 2; b = 2; 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, -1.31, -1.30}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198126 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .68, .69}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198127 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 22 2011