A199174 - OEIS

%I #12 Aug 03 2021 14:25:29

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

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

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

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

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

%e negative: -1.67892976349109451959338320116343299...

%e positive:  1.90253038503823570345779582773972676...

%t a = 1; b = 1; 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]   (* A199174 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.90, 1.91}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199175 *)

%Y Cf. A199170, A199175.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 04 2011

%E a(84) onwards corrected by _Georg Fischer_, Aug 03 2021