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

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

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

%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: 0.672255167738256880748604617870325976...

%e greatest x: 3.525867901227958617954825081711394...

%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, 0, 4}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, .65, .68}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198098 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198099 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 21 2011