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

%I #8 Aug 03 2021 14:31:33

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

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

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

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

%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.

%e x=0.6655990773306761525052651922688530...

%t a = 3; b = 1; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -1, 1.5}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .66, .67}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199664 *)

%Y Cf. A199597.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 09 2011

%E a(88) onwards corrected by _Georg Fischer_, Aug 03 2021