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

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

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

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

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

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

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

%e least x: 0.3544963674136767044773458959502707334...

%e greatest x: 3.2993291450362846931582114018079102408...

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

%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]

%t Plot[{f[x], g[x]}, {x, -1, 4}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, -.4, -.3}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A197825 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A197831 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 20 2011