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A198811 Decimal expansion of x>0 satisfying x^2+2*cos(x)=4. 2

%I #6 Mar 30 2012 18:57:56

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

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

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

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

%C See A198755 for a guide to related sequences. The Mathematica program includes a graph.

%e x=2.3135893490484879224453041336666...

%t a = 1; b = 2; c = 4;

%t f[x_] := a*x^2 + b*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, 2.3, 2.4}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198811 *)

%Y Cf. A198755.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 30 2011

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