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A199270 Decimal expansion of x>0 satisfying 2*x^2+2*x*cos(x)=1. 3

%I

%S 3,8,1,7,4,8,4,2,0,9,9,2,9,8,5,9,5,7,9,1,8,5,2,1,6,1,1,8,2,3,4,8,6,6,

%T 4,5,5,9,3,3,4,1,8,5,5,0,7,6,7,1,7,8,3,1,6,0,6,3,2,9,9,1,9,0,3,7,7,0,

%U 9,1,5,4,0,8,1,6,0,9,0,2,1,1,1,5,3,4,5,2,9,4,7,9,7,3,1,8,5,8,5

%N Decimal expansion of x>0 satisfying 2*x^2+2*x*cos(x)=1.

%C See A199170 for a guide to related sequences. The Mathematica program includes a graph.

%e negative: -1.017240798342455566560350070545346176017411...

%e positive: 0.381748420992985957918521611823486645593341...

%t a = 2; b = 2; c = 1;

%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -1.1, -1.0}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199269 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .38, .39}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199270 *)

%Y Cf. A199170.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 04 2011

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Last modified February 27 03:50 EST 2020. Contains 332299 sequences. (Running on oeis4.)