OFFSET
0,2
COMMENTS
Ramanujan's question 525 (ii), see Berndt and Rankin in References: Show how to find the square roots of surds of the form A^(1/3) + B^(1/3), and hence prove that sqrt(28^(1/3)-27^(1/3)) = (98^(1/3)-28^(1/3)-1)/3.
Real root of x^3 + x^2 + 5*x - 1 = 0. - Hugo Pfoertner, Sep 12 2018
REFERENCES
B. C. Berndt and R. A. Rankin, Ramanujan: Essays and Surveys, American Mathematical Society, 2001, ISBN 0-8218-2624-7, page 221 (JIMS 6, page 39 and pages 191-192).
Srinivasa Ramanujan, Collected Papers, Chelsea, 1962, page 327, Question 525.
EXAMPLE
0.191282440060928016751295506478335098972307207254571910553771150812505...
MAPLE
evalf(sqrt(28^(1/3)-27^(1/3))); # Muniru A Asiru, Aug 28 2018
MATHEMATICA
RealDigits[Sqrt[28^(1/3) - 27^(1/3)], 10, 120][[1]] (* Amiram Eldar, Jun 27 2023 *)
PROG
(PARI) sqrt(28^(1/3)-27^(1/3))
(PARI) p(x)=x^3+x^2+5*x-1;
solve(x=0.18, 0.20, p(x)) \\ Hugo Pfoertner, Sep 12 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Aug 28 2018
STATUS
approved