Αποτελέσματα Αναζήτησης
25 Ιαν 2019 · $\alpha ^2+\beta^2+\gamma^2=(\alpha +\beta+\gamma)^2-2(\alpha \beta+\beta \gamma+\alpha \gamma)=4-2(\alpha \beta+\beta \gamma+\alpha \gamma)$ I am not sure how to figure out $2(\alpha \beta+\beta \gamma+\alpha \gamma)$ term.I am not going for long method of finding eigen values by characteristic polynomial since this question came in $2$ marks ...
5 Αυγ 2015 · Using the root-coefficient relationship, we have the following: $$\alpha + \beta + \gamma = -1,$$ $$\alpha\beta\gamma = -1,$$ $$\alpha\beta + \beta\gamma + \gamma ...
1 Ιουλ 2021 · For example if take $\beta,\delta$ to be positive and $\gamma$ to be negative and then apply power-mean inequality we get $$\left({\beta+\delta\over 2}\right)^n\le{\left(\beta+\gamma+\delta \right)^n+(-\gamma)^n\over2}={\beta^n+\delta^n\over2}$$ What we get is basically the power-mean inequality applied to $\beta$ and $\delta$ and nothing new.
12 Οκτ 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
19 Δεκ 2018 · Cases of $\alpha^{'}\geq 5$ included cases of any of the other three ($\beta'\leq6;\gamma'\leq5;\delta'\leq6$) not following together with or putting similar argument for other three conditions, we can contemplate that all in all $4\times 3=12$ terms are already subtracted and that we need to now add the "at least two disobeyed condition cases ...
12 Οκτ 2019 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
14 Απρ 2019 · $\begingroup$ Your previous to last $\delta$ should be $\gamma$. It may be worth pointing out that for any $\alpha$, $\alpha<\beta+(\alpha+1)$, and so you get that in fact any ordinal $\alpha\ge\beta$ has the form $\beta+\delta$ for some $\delta$. $\endgroup$
28 Οκτ 2020 · Show that $\alpha^2-3(1+\sqrt{10})\alpha+4=0$, and find similar quadratic equations satisfied by $\beta$, $\gamma$ and $\delta$. Unsure how to approach this question. So far I have:
1 Σεπ 2013 · But more importantly, what summations do the expressions $$\sum \alpha,\qquad \sum\alpha\beta$$ represent? $\alpha$ and $\beta$ are specific numbers, not variables. It'd be like writing $$\sum 5$$ What does that mean? $\endgroup$
11 Ιουλ 2020 · Also $\alpha\beta+\beta\gamma+\gamma\alpha=-\alpha\beta\gamma$ so, yes, I can see why you are asking...$\alpha^3+\beta^3+\gamma^3=3\alpha\beta\gamma$ $\endgroup$ – Martin Hansen Commented Jul 11, 2020 at 15:30
