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

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

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

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

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

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

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

%e least x: -1.77323215749171672703899464197081641...

%e greatest x: 0.620762336586614714452120247321515...

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

%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, -1.8, -1.7}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A197843 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .62, .63}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A197844 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 20 2011