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

%I #7 Aug 09 2021 07:45:47

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

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

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

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

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

%e least x: -1.0119640719541596551643922516868104...

%e greatest x: 0.4003039952551859146306371868342035...

%t a = 4; b = 3; 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, -1.1, -1.0}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198363 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .4, .41}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198364 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 24 2011