2006-06-30 08:03:48 · 3 answers · asked by kukur_diamond 1 in Science & Mathematics ➔ Mathematics
a = 3^(1/3)
b = 4^(1/3)
c = a+b
If you use the primitive element theorem you will see that c is a primitive element for Q(a)(b)
so Q(a)(b)=Q(c), which implies that the degree of the minimal polynomial is 3*3 = 9
By primitive element theorem a is written as a rational fraction in c, a = f/g(c),
so a^3 = f/g^3(c), or g^3(c)*a^3 = f^3(c), g and f polynomials in Q.
so the minimal polynomial will be 3g^3-f^3
( hoping that g and f have at most degree 3 in c)
g and f can be computed as in the proof of primitive element theorem
i.e compute gcd (x^3-3, (c-x)^3-4))
Maybe there is a better way...
2006-06-30 13:09:57 · answer #1 · answered by Theta40 7 · 0⤊ 0⤋
wow i was going to try to answer your question by looking up minimal polynomials... yeah i have no idea! What math are you in? is that calculus it looks scary!
2006-06-30 08:08:53 · answer #2 · answered by j h 2 · 0⤊ 0⤋
Is it a Big Mac with fries?
2006-06-30 08:07:30 · answer #3 · answered by KingCucamonga 5 · 0⤊ 0⤋