login
Decimal expansion of x>0 satisfying 3*x^2+3*x*cos(x)=1.
3

%I #8 Feb 07 2025 16:44:05

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

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

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

%N Decimal expansion of x>0 satisfying 3*x^2+3*x*cos(x)=1.

%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: -0.942013171745925470278385478816333...

%e positive: 0.2701502896318032580209778461269860...

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

%t f[x_] := a*x^2 + b*x*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, -1, -.9}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199291 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .27, .28}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199292 *)

%Y Cf. A199170.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Nov 05 2011