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A199173 Decimal expansion of x>0 satisfying x^2+x*cos(x)=2.

%I A199173 #8 Feb 07 2025 16:44:05
%S A199173 1,2,7,6,6,7,1,3,6,7,9,4,0,7,6,0,5,5,4,0,9,1,5,0,7,4,9,0,4,4,1,2,1,0,
%T A199173 2,7,8,3,4,0,0,2,4,6,4,7,3,4,5,6,7,6,0,6,1,5,6,6,2,8,7,6,7,4,1,2,5,9,
%U A199173 6,3,2,8,0,1,0,9,7,6,3,1,1,9,2,3,4,4,1,8,2,9,4,3,2,4,2,4,5,7,8
%N A199173 Decimal expansion of x>0 satisfying x^2+x*cos(x)=2.
%C A199173 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199173 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199173 negative: -1.4669783053971235684198141847804443...
%e A199173 positive:  1.27667136794076055409150749044121027834...
%t A199173 a = 1; b = 1; c = 2;
%t A199173 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199173 Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
%t A199173 r = x /. FindRoot[f[x] == g[x], {x, -1.5, -1.3}, WorkingPrecision -> 110]
%t A199173 RealDigits[r]  (* A199172 *)
%t A199173 r = x /. FindRoot[f[x] == g[x], {x, 1.27, .28}, WorkingPrecision -> 110]
%t A199173 RealDigits[r]  (* A199173 *)
%Y A199173 Cf. A199170.
%K A199173 nonn,cons
%O A199173 1,2
%A A199173 _Clark Kimberling_, Nov 04 2011