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

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

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

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

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

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

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

%e least x: 0.69658584777906580198659243463275435885...

%e greatest x: 4.28804762370313657874580002787893697...

%t a = 1; 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, 5}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, 0.69, 0.70}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198144 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, 4.28, 4.29}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198145 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 21 2011