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

%I #5 Mar 30 2012 18:57:54

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

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

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

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

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

%e least x: -0.91555432657358705292706966750136951...

%e greatest x: 0.7424374889656033785172455301643263...

%t a = 4; b = 1; c = 4;

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

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

%t r1 = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198355 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .74, .75}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198356 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 24 2011