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%I #5 Mar 30 2012 18:57:53
%S 1,7,2,8,0,7,8,0,8,6,2,5,3,1,4,2,1,7,1,3,9,7,2,4,5,4,3,2,4,2,4,7,6,8,
%T 2,6,7,7,6,2,0,8,0,6,2,0,8,4,3,1,3,3,5,4,1,6,2,6,1,2,4,2,5,1,3,8,6,4,
%U 1,6,9,0,4,2,6,1,7,0,0,3,8,7,3,5,0,7,3,9,8,9,6,7,6,4,8,6,2,4,4
%N Decimal expansion of least x having x^2+2x=3*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: -1.72807808625314217139724543242476826...
%e greatest x: 0.773696189243809421714739053530453...
%t a = 1; b = 2; c = 3;
%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, -1.8, -1.7}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A197845 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, .77, .78}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A197846 *)
%Y Cf. A197737.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Oct 20 2011