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A199189 Decimal expansion of x>0 satisfying 2*x^2+x*cos(x)=1. 4

%I

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

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

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

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

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

%e negative: -0.883330197195891938925896450885677107...

%e positive: 0.522945946113111737247623836359811237139...

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

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

%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.84, -.83}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199188 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .52, .53}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199189 *)

%Y Cf. A199170.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 04 2011

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Last modified February 17 21:46 EST 2020. Contains 332006 sequences. (Running on oeis4.)