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A199175 Decimal expansion of x>0 satisfying x^2+x*cos(x)=3.

%I A199175 #8 Feb 07 2025 16:44:05
%S A199175 1,9,0,2,5,3,0,3,8,5,0,3,8,2,3,5,7,0,3,4,5,7,7,9,5,8,2,7,7,3,9,7,2,6,
%T A199175 7,6,1,2,7,8,9,4,2,9,0,5,3,3,4,2,2,1,0,6,0,4,5,0,4,0,1,9,1,2,0,5,8,8,
%U A199175 0,3,8,0,5,8,5,3,8,0,4,9,5,5,8,4,2,9,9,7,5,1,4,1,6,2,8,9,5,1,0
%N A199175 Decimal expansion of x>0 satisfying x^2+x*cos(x)=3.
%C A199175 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199175 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199175 negative: -1.67892976349109451959338320116343299...
%e A199175 positive:  1.90253038503823570345779582773972676...
%t A199175 a = 1; b = 1; c = 3;
%t A199175 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199175 Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
%t A199175 r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]
%t A199175 RealDigits[r]   (* A199174 *)
%t A199175 r = x /. FindRoot[f[x] == g[x], {x, 1.90, 1.91}, WorkingPrecision -> 110]
%t A199175 RealDigits[r]  (* A199175 *)
%Y A199175 Cf. A199170.
%K A199175 nonn,cons
%O A199175 1,2
%A A199175 _Clark Kimberling_, Nov 04 2011