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%I #6 Mar 30 2012 18:57:53
%S 7,8,8,3,9,6,8,4,5,9,9,2,9,6,5,4,2,9,0,7,8,8,2,0,9,8,3,9,8,2,0,0,1,9,
%T 1,2,2,9,5,5,1,8,7,5,3,5,3,1,2,0,4,9,1,8,6,5,0,5,6,6,5,9,8,2,7,0,6,7,
%U 8,7,2,5,7,2,4,8,7,8,1,4,6,0,0,8,8,9,3,3,7,6,7,8,6,9,8,6,2,8,2
%N Decimal expansion of x>0 having x^2+x=2*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e negative: -1.3405253081973984478676062849960660920583...
%e positive: 0.7883968459929654290788209839820019122955...
%t a = 1; 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, 1.5}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, -1.5, -1.3}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A197809 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, .78, .79}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A197810 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 20 2011
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