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Decimal expansion of the real root of 2*x^3 + x - 1.
1

%I #16 Feb 04 2024 15:42:39

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

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

%U 8,0,2,4,1,5,7,7

%N Decimal expansion of the real root of 2*x^3 + x - 1.

%F Equals (1/6)*(54+6*sqrt(87))^(1/3) - 1/(54+6*sqrt(87))^(1/3).

%F Equals ((54 + 6*sqrt(87))^(1/3) - (54 - 6*sqrt(87))^(1/3)*(1-sqrt(3)*i)/2)/6, with i the imaginary unit sqrt(-1).

%F Equals -sqrt(2/3) * sinh(log((sqrt(58) - 3*sqrt(6))/2)/3). - _Vaclav Kotesovec_, Aug 19 2022

%e 0.5897545123014583842788017470960713624514351732283620723880793412350480241...

%t First[RealDigits[N[Root[-1+#1+2 #1^3 &, 1, 0], 76]]] (* _Stefano Spezia_, Aug 19 2022 *)

%o (PARI) solve(x=0, 1, 2*x^3 + x - 1) \\ _Michel Marcus_, Aug 19 2022

%Y Cf. A356030.

%K nonn,cons,easy

%O 0,1

%A _Wolfdieter Lang_, Aug 19 2022