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A199174 Decimal expansion of x < 0 satisfying x^2 + x*cos(x) = 3.

%I A199174 #15 Feb 07 2025 16:44:05
%S A199174 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 A199174 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 A199174 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 A199174 Decimal expansion of x < 0 satisfying x^2 + x*cos(x) = 3.
%C A199174 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199174 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199174 negative: -1.67892976349109451959338320116343299...
%e A199174 positive:  1.90253038503823570345779582773972676...
%t A199174 a = 1; b = 1; c = 3;
%t A199174 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199174 Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
%t A199174 r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]
%t A199174 RealDigits[r]   (* A199174 *)
%t A199174 r = x /. FindRoot[f[x] == g[x], {x, 1.90, 1.91}, WorkingPrecision -> 110]
%t A199174 RealDigits[r]  (* A199175 *)
%Y A199174 Cf. A199170, A199175.
%K A199174 nonn,cons
%O A199174 1,2
%A A199174 _Clark Kimberling_, Nov 04 2011
%E A199174 a(84) onwards corrected by _Georg Fischer_, Aug 03 2021