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Decimal expansion of the number x satisfying x^2+8=e^x.
2

%I #8 Feb 07 2025 16:44:07

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

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

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

%N Decimal expansion of the number x satisfying x^2+8=e^x.

%C See A201741 for a guide to related sequences. The Mathematica program includes a graph.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e x=2.7420571972586515955191673787900235851680254...

%t a = 1; b = 0; c = 8;

%t f[x_] := a*x^2 + b*x + c; g[x_] := E^x

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 2.7, 2.8}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201747 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 05 2011