Find $\gamma$ such that $\mathbb{Q}(\gamma)=\mathbb{Q}(\alpha,\beta)$ where $\alpha$ is a root of $x^3-2x+3$ and $\beta$ is a root of $x^2+x+2$?
1914
General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
104321
Prove that $1 + \cos\alpha + \cos\beta + \cos\gamma = 0$
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
142470
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$ ??
3563
Find all roots of $\,x^2\!\equiv x\pmod{\!900}$, i.e all idempotents in $\Bbb Z_{900}$
158588
Determine the Galois group of the polynomial $(x^3-2)(x^3-3)(x^2-2)$ over $\mathbb{Q}(\sqrt {-3})$
61343
Prove that if $\alpha, \beta, \gamma$ are angles in triangle, then $(tan(\frac{\alpha}{2}))^2+(tan(\frac{\beta}{2}))^2+(tan(\frac{\gamma}{2}))^2\geq1$
148876
What is the meaning of $\mathbf{Q}(\sqrt{2},\sqrt{3})$
109223
For ordinals $\delta$ and $\beta$, if $\delta\in$ or $=\beta$, then there exists $\gamma\in$ or $=\beta$ such that $\beta=\delta+\gamma$
104145
Finding the value of $3(\alpha-\beta)^2$ if $\int_0^2 f(x)dx=f(\alpha) +f(\beta)$ for all $f$
55197
Roots of $ x^3-3x+1$
157710
$x^{3}-x-2=0$ how do I find the roots?
157496
Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$
68838
Why $\sqrt[3]{3}\not\in \mathbb{Q}(\sqrt[3]{2})$?
82262
minimal polynomial of nth root of 2 over $\mathbb Q$