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%I #5 Mar 30 2012 18:57:54
%S 4,2,8,8,0,4,7,6,2,3,7,0,3,1,3,6,5,7,8,7,4,5,8,0,0,0,2,7,8,7,8,9,3,6,
%T 9,7,4,6,5,9,5,3,7,8,2,3,7,0,2,3,6,5,0,1,5,5,8,5,6,6,2,1,8,9,2,2,3,3,
%U 0,1,5,6,0,6,6,1,5,1,5,5,9,1,5,4,8,6,9,7,8,7,5,4,5,1,9,7,5,4,1
%N Decimal expansion of greatest 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: 4.2880476237031365787458000278789369746...
%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 1,1
%A _Clark Kimberling_, Oct 21 2011
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