Search found 751 matches
- Wed Dec 08, 2010 11:32 am
- Forum: Algebra
- Topic: Find value using the roots of polynomial
- Replies: 5
- Views: 5056
Re: Find value using the roots of polynomial
Remember, one of the main purpose of the forum is to practice writing formal solutions.
- Wed Dec 08, 2010 3:34 am
- Forum: Social Lounge
- Topic: Mila in BdMO National
- Replies: 31
- Views: 19936
Mila in BdMO National
Do you want to see Mila in BdMO National Olympiad? Let us know what you are thinking.
- Wed Dec 08, 2010 3:24 am
- Forum: Algebra
- Topic: Find value using the roots of polynomial
- Replies: 5
- Views: 5056
Find value using the roots of polynomial
It is most probably Canada 1995. Quite nice, and medium difficulty problem. Try it!
If $\alpha,\beta,\gamma$ are roots of $x^3-x-1$, then find
\[\frac{\alpha-1}{\alpha+1}+\frac{\beta-1}{\beta+1}+\frac{\gamma-1}{\gamma+1}\]
If $\alpha,\beta,\gamma$ are roots of $x^3-x-1$, then find
\[\frac{\alpha-1}{\alpha+1}+\frac{\beta-1}{\beta+1}+\frac{\gamma-1}{\gamma+1}\]
- Wed Dec 08, 2010 2:34 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO Higher secondary solutions
- Replies: 13
- Views: 14584
Re: BdMO Higher secondary solutions
আচ্ছা একটা ভাল কথা। এইখানে সবাই কি গাইড লাইনটা পড়ে দেখেছ? আর LaTeX font install করেছ?
- Tue Dec 07, 2010 11:32 pm
- Forum: News / Announcements
- Topic: 50 user mark achieved
- Replies: 1
- Views: 3129
50 user mark achieved
We have achieved 50 users mark. I believe that for any forum crossing 50 members at the very first day is a huge achievement. Thanks everyone!
Our $50^{\text{th}}$ member is fractal. Congratulations to him/her being a part of the history.
Our $50^{\text{th}}$ member is fractal. Congratulations to him/her being a part of the history.
- Tue Dec 07, 2010 9:56 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO 2010 H. Sec. problem 8
- Replies: 22
- Views: 14715
BdMO 2010 H. Sec. problem 8
Find all prime numbers $p$ and integers $a$ and $b$ (not necessarily positive) such that $p^a + p^b$
is the square of a rational number.
is the square of a rational number.
- Tue Dec 07, 2010 9:53 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO Higher secondary solutions
- Replies: 13
- Views: 14584
Re: BdMO Higher secondary solutions
This is the Problem: BdMO 2010, Higher Sec. ,problem 9. Find the number of odd coefficients in expansion of $(x + y)^{2010}$. I solve the problem using Lucus Theorem . Lucus Theorem actually KILLS the problem. Abir vi showed me another "elementary" way. I think that Avik vi can show us that solution...
- Tue Dec 07, 2010 9:03 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO Higher secondary solutions
- Replies: 13
- Views: 14584
Re: BdMO Higher secondary solutions
Masum, I think that she would appreciate more if you give us a full solution, not just the answer.
- Tue Dec 07, 2010 9:02 pm
- Forum: Number Theory
- Topic: Find largest x
- Replies: 3
- Views: 4096
Re: Find largest x
Good Job!
Zzzz, I guess, I (we all) know you.
Zzzz, I guess, I (we all) know you.
- Tue Dec 07, 2010 8:59 pm
- Forum: Geometry
- Topic: Geometry Marathon v1.0
- Replies: 23
- Views: 16533
Geometry Marathon v1.0
I think that we can start a marathon here. The rule is very simple. I start this marathon with a problem. If someone solve it, s/he must submit another problem. This way the marathon will go on. The difficulty level of the problems should be around National Olympiad medium level. Here goes the first...