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Decimal expansion of the number x satisfying x^2+3x+4=e^x.
2

%I #7 Jan 30 2025 11:34:15

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

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

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

%N Decimal expansion of the number x satisfying x^2+3x+4=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=3.1525907367571582749969890047671397858138094...

%t a = 1; b = 3; c = 4;

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

%t Plot[{f[x], g[x]}, {x, -3, 3.3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.2}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201901 *)

%Y Cf. A201741.

%K nonn,cons,changed

%O 1,1

%A _Clark Kimberling_, Dec 06 2011