Matematické Fórum

stuart clark · 26. 08. 2019 08:09

If $\alpha$ is the root of the equation $x^3-x-1=0$ ,

Then value of
$(3\alpha^2-4\alpha)^{\frac{1}{3}}+(3\alpha^2+4\alpha+2)^{\frac{1}{3}}.$

laszky · 28. 08. 2019 01:29

↑ stuart clark:

Hi,

check_drummer · 29. 08. 2019 22:45

↑ laszky:
Hi, but is the value of $x^{\frac{1}{3}}$ uniquelly determined?

laszky · 30. 08. 2019 14:06

↑ check_drummer:

Ok, you are right. We shall consider only the real root of the equation and only a real cube root.

vanok · 30. 08. 2019 20:01

Hi ↑ laszky:,
Have you studied this problem in the case of finite fields with $p^3$ ( p prime) elements?

stuart clark · 17. 09. 2019 08:51

Thanks ↑ laszky:

Answer given as $2$

#1 26. 08. 2019 08:09