MathDB

4

Part of 2017 QEDMO 15th

Problems(2)

a^3 +1/a^3=? and a^5 +1/a^5 =? if (a+1/a)^2=11

Source: 15th -a QEDMO problem 4 (19. - 22. 10. 2017) https://artofproblemsolving.com/community/c1512515_qedmo_2005

5/29/2021
Let aa be a real number such that (a+1a)2=11\left(a + \frac{1}{a}\right)^2=11. What possible values can a3+1a3a^3 + \frac{1}{a^3} and a5+1a5a^5 + \frac{1}{a^5} take?
algebra
image f ([a, b]) is interval of length b - a.

Source: 15th -b QEDMO problem 4 (19. - 22. 10. 2017) https://artofproblemsolving.com/community/c1512515_qedmo_2005

5/30/2021
Find all functions f:R→Rf: R \to R for which the image f([a,b])f ([a, b]) for all real a≤ba \le b is (not necessarily closed!) interval of length b−ab - a.
functional equationfunctionalalgebra