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A199051 Decimal expansion of x>0 satisfying x^2+2*sin(x)=3.

%I A199051 #8 Feb 07 2025 16:44:05
%S A199051 1,1,0,2,4,4,0,9,9,2,7,8,2,4,7,4,5,0,2,9,0,0,5,1,2,3,2,6,9,5,8,5,7,9,
%T A199051 1,1,5,6,4,4,2,2,5,6,9,1,4,6,4,3,4,4,8,9,0,7,6,6,8,5,2,3,7,9,8,9,4,1,
%U A199051 3,6,3,8,1,2,7,7,3,5,7,8,6,7,0,0,8,0,5,9,3,6,5,3,8,3,1,6,7,5,9
%N A199051 Decimal expansion of x>0 satisfying x^2+2*sin(x)=3.
%C A199051 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199051 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199051 negative: -2.159478296974116018268923878524689009...
%e A199051 positive:  1.1024409927824745029005123269585791156...
%t A199051 a = 1; b = 2; c = 3;
%t A199051 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199051 Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
%t A199051 r = x /. FindRoot[f[x] == g[x], {x, -2.2, -2.1}, WorkingPrecision -> 110]
%t A199051 RealDigits[r] (* A199050 *)
%t A199051 r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
%t A199051 RealDigits[r](* A199051 *)
%Y A199051 Cf. A198866.
%K A199051 nonn,cons
%O A199051 1,4
%A A199051 _Clark Kimberling_, Nov 02 2011