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%I #5 Mar 30 2012 18:57:54
%S 5,4,1,4,1,8,9,0,3,1,7,2,9,0,6,7,1,1,2,9,6,9,2,1,9,6,7,2,0,6,2,4,0,6,
%T 8,8,1,3,3,0,1,8,0,6,2,4,3,1,5,2,0,5,6,5,0,4,8,8,9,6,6,8,2,9,7,8,2,6,
%U 1,4,2,2,3,2,8,8,0,0,0,9,7,6,7,7,5,3,2,3,7,8,4,3,1,9,8,9,3,9,1
%N Decimal expansion of greatest x having 4*x^2+x=2*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: -0.74421989852706246873275828006370...
%e greatest x: 0.541418903172906711296921967206240...
%t a = 4; b = 1; c = 2;
%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, -.8, -.7}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A198351 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A198352 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 23 2011
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