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

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

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

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

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

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

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

%e least x: -2.38894934360890459687043267819730...

%e greatest x: 0.5010411864464903833151417790663...

%t a = 1; b = 3; c = 2;

%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, -2.4, -2.3}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198104 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .5, .51}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198105 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 21 2011