Hey, i'm having trouble on how to tackle this question "Prove that the number 2^(1/3)+3^(1/2) is algebraic"
I know i have to show it as a polynomial but I don't know where to begin.
Any help would be appreciated
Thanks
Hey, i'm having trouble on how to tackle this question "Prove that the number 2^(1/3)+3^(1/2) is algebraic"
I know i have to show it as a polynomial but I don't know where to begin.
Any help would be appreciated
Thanks
Let $\displaystyle x=2^{1/3}+3^{1/2}$. Then for any positive integer n, the number $\displaystyle x^n$ is a linear combination with rational coefficients of some fixed numbers $\displaystyle \{a_1,\dots,a_k\}$. Find these $\displaystyle a_k$, and, in particular, k. This means that k + 1 numbers $\displaystyle 1=x^0$, $\displaystyle x$, $\displaystyle x^2$, ..., $\displaystyle x^k$ are linearly dependent over $\displaystyle \mathbb{Q}$. What does this mean?
Edit: I did not notice that this is a pre-university forum, so you may not know about linear dependence. Please say if the description above makes sense to you.