A199180 - OEIS

%I #7 Jan 30 2025 16:07:51

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

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

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

%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.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%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,changed

%O 1,2

%A _Clark Kimberling_, Nov 04 2011