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%I #5 Mar 30 2012 18:57:53
%S 6,6,9,9,6,8,1,6,9,0,4,6,9,3,3,1,9,1,7,5,0,9,3,9,2,8,9,5,6,2,1,6,6,2,
%T 8,7,2,9,5,4,9,4,3,5,5,1,3,5,9,1,9,9,5,8,3,7,3,0,9,3,3,7,4,7,0,7,4,6,
%U 7,7,9,1,4,4,7,9,6,2,4,3,1,3,5,0,2,7,7,8,0,6,1,6,6,2,4,5,8,4,1
%N Decimal expansion of greatest x having 2*x^2+x=2*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: -1.01705490067506096933116558361774...
%e greatest x: 0.66996816904693319175093928956216628...
%t a = 2; b = 1; 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, -1.02, -1.01}, WorkingPrecision -> 110]
%t RealDigits[r1](* A198114 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, .66, .67}, WorkingPrecision -> 110]
%t RealDigits[r2](* A198115 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 21 2011
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