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 A202300 Decimal expansion of the real root of x^3 + 2x^2 + 10x - 20. 1
 1, 3, 6, 8, 8, 0, 8, 1, 0, 7, 8, 2, 1, 3, 7, 2, 6, 3, 5, 2, 2, 7, 4, 1, 4, 3, 3, 0, 0, 2, 1, 3, 2, 5, 5, 3, 9, 5, 4, 2, 4, 3, 5, 5, 4, 1, 4, 8, 7, 5, 3, 6, 5, 3, 0, 7, 9, 3, 7, 1, 2, 6, 9, 0, 2, 1, 8, 2, 6, 3, 1, 4, 7, 4, 1, 9, 6, 8, 8, 3, 8, 1, 9, 6, 9, 3, 9, 8, 8, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS There is a small typo in Posamentier & Lehmann (2007): this number is given as approximately 1.3688081075 rather than 1.3688081078, a mistake that can't be justified by rounding rather than truncating nor a loss of machine precision. - Alonso del Arte, Mar 24 2012 Perhaps the reason for the mistake is that the authors got the correct answer mixed up with Fibonacci's answer, which, though wrong, was very good for the time: 1 + 22/60 + 7/60^2 + 42/60^3 + 33/60^4 + 4/60^5 + 40/60^6 = 1.36880810785322... But apparently they truncated at the first 5 and left out the 8 before that 5. - Alonso del Arte, Jun 09 2014 The complex roots are -1.68440405391... +- 3.43133135... * i. - Alonso del Arte, Jun 21 2014 REFERENCES John Derbyshire, Unknown Quantity: A Real and Imaginary History of Algebra. Washington, DC: Joseph Henry Press (2006): 69-70. Julian Havil, The Irrationals, A Story of the Numbers You Can't Count On, Princeton University Press, Princeton and Oxford, 2012, pp. 63-64. Alfred S. Posamentier & Ingmar Lehmann, The (Fabulous) Fibonacci Numbers. New York: Prometheus Books (2007) p. 21. LINKS Ezra Brown and Jason C. Brunson, Fibonacci's forgotten number Stanislaw Glushkov, On approximation methods of Leonardo Fibonacci, Historia Mathematica 3 (1976), pp. 291-296. Wolfram|Alpha, real root of x^3 + 2x^2 + 10x - 20 = 0 FORMULA x = (2*sqrt(3930)/9 - 352/27)^(1/3) + (2*sqrt(3930)/9 + 352/27)^(1/3) - 2/3; x = (1/3)*(-2 - 13 * 2^(2/3)/(176 + 3*sqrt(3930))^(1/3) + (2*(176 + 3*sqrt(3930)))^(1/3)). The first formula comes from Posamentier & Lehmann (2007), the second from Wolfram|Alpha. - Alonso del Arte, Mar 24 2012 EXAMPLE x = 1.36880810782137263522741433002132553954243554148753653... MATHEMATICA RealDigits[x /. FindRoot[x^3 + 2x^2 + 10x - 20 == 0, {x, 1.4}, WorkingPrecision -> 120]][] (* Harvey P. Dale, Feb 27 2013 *) PROG (PARI) real(polroots(x^3+2*x^2+10*x-20)) (PARI) polrootsreal(x^3+2*x^2+10*x-20) \\ Charles R Greathouse IV, Jan 05 2016 CROSSREFS Cf. A159990, A243629, A244467. Sequence in context: A248760 A011261 A104541 * A244467 A200590 A329510 Adjacent sequences:  A202297 A202298 A202299 * A202301 A202302 A202303 KEYWORD nonn,cons AUTHOR Charles R Greathouse IV, Jan 11 2012 STATUS approved

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Last modified June 23 02:02 EDT 2021. Contains 345395 sequences. (Running on oeis4.)