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%I #5 Mar 30 2012 18:57:57
%S 1,5,0,9,3,3,9,0,6,2,4,6,6,6,8,8,1,2,3,4,5,1,2,5,2,6,4,1,7,9,2,1,9,0,
%T 2,9,3,1,3,5,1,6,4,6,6,5,1,7,1,9,2,6,5,2,8,1,2,4,9,8,7,7,9,1,9,8,7,3,
%U 9,5,1,1,6,8,3,1,7,7,2,1,7,8,5,5,1,2,9,3,6,1,0,0,6,4,5,1,9,4,3
%N Decimal expansion of least x satisfying x^2+3*x*cos(x)=2.
%C See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%e least: -1.5093390624666881234512526417921902931351...
%e greatest: 3.44428460990495541079195552785381251956...
%t a = 1; b = 3; c = 2;
%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -1.6, -1.5}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199184 least of four roots *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.44, 3.45}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199185 greatest of four roots *)
%Y Cf. A199170.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 04 2011