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Decimal expansion of greatest x having 2*x^2-4x=-3*cos(x).
3

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

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

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

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

%N Decimal expansion of greatest x having 2*x^2-4x=-3*cos(x).

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

%e least x: 0.85876971369761442119310432181053308611...

%e greatest x: 2.4766169740668170810192726417322477...

%t a = 2; b = -4; c = -3;

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

%t Plot[{f[x], g[x]}, {x, -1, 3}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, .85, .86}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198136 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, 2.4, 2.5}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198137 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 22 2011