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A199274 Decimal expansion of x>0 satisfying 2*x^2+3*x*cos(x)=1. 3

%I

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

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

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

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

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

%e negative: -1.11270716122321939210526043888351330910...

%e positive: 0.289505448385867415592179483198982452381...

%t a = 2; b = 3; 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, -1.2, -1.1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199273 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .28, .29}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199274 *)

%Y Cf. A199170.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 04 2011

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)