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A199181 Decimal expansion of x>0 satisfying x^2+2*x*cos(x)=3. 4

%I #5 Mar 30 2012 18:57:57

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

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

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

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

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

%e negative: -1.6524280450417421424058918662580123...

%e positive: 2.980645279438536834594908905579032175...

%t a = 1; b = 2; c = 3;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199180 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 2.98, 2.99}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199181 *)

%Y Cf. A199170.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Nov 04 2011

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Last modified March 28 04:05 EDT 2024. Contains 371235 sequences. (Running on oeis4.)