Search found 78 matches
- Tue Mar 01, 2011 9:54 pm
- Forum: Higher Secondary Level
- Topic: Khalifa's Law!
- Replies: 8
- Views: 6917
Re: Khalifa's Law!
You find in any coordinate geometry books in honours specially the books of national university.
- Wed Feb 16, 2011 2:08 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Secondary 2011/9
- Replies: 11
- Views: 9069
Re: BdMO National Secondary 2011/9
However, I think I've solved it. But, I'm not sure. Ok, if I'm wrong then correct me. Here's my solution: Suppose, (3^1/2+2^1/2)^1/100=x Then, we can easily show that, (3^1/2-2^1/2)^1/100=1/x We can easily show that x and 1/x are individually irrational. Now, we suppose that (x+1/x) is not irration...
- Mon Feb 14, 2011 11:27 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2011/10
- Replies: 3
- Views: 3611
Re: BdMO National Higher Secondary 2011/10
Let $n=2x+1$ then try to prove that $(x+1)(x+1)$ is the maximum number of black square in the $n^2$ square of the grid.Now find the value of white square. $q^2=(2x+1)^2-(x+1)^2$ Then by solving equation show that $1+3q^2$ is must be perfect square and also $1$ modulo to $3$. Then complete the prove ...
- Mon Feb 14, 2011 10:10 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Secondary 2011/9
- Replies: 11
- Views: 9069
Re: BdMO National Secondary 2011/9
At first we should try to do this a+1/a is rational then a^n+(1/a)^n must rational.
Now according to the question a^100+(1/a)^100 is irrational.
So a+1/a is is irrational.
Now according to the question a^100+(1/a)^100 is irrational.
So a+1/a is is irrational.
- Mon Feb 14, 2011 10:00 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2011/8
- Replies: 18
- Views: 11722
Re: BdMO National Higher Secondary 2011/8
TIURMI what do you mean by this?
- Mon Feb 14, 2011 1:09 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2011/8
- Replies: 18
- Views: 11722
Re: BdMO National Higher Secondary 2011/8
As D is the mid point of BC then AD=BD=CD.GB andAD is parallel.SO that<DAB=<ABG AD=BD,<ABC=<ABG.Now we can prove that the triangle ABC and GBA is equal.Let the extention of CF meets BC at I.So CI,GD,AB is a median of the triangle GBC. Now by Cevas theorem in triangle GDC GF.DR.CA=FD.RC.AG We know th...
- Mon Feb 14, 2011 12:33 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2011/8
- Replies: 18
- Views: 11722
Re: BdMO National Higher Secondary 2011/8
Fahim you are right............and i am senior to you
- Sun Feb 13, 2011 11:12 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Secondary 2011/9
- Replies: 11
- Views: 9069
Re: BdMO National Secondary 2011/9
Sorry you are incorrect.why the 100th power needed to be equal?Try to prove that if a+1/a is rational then a^n+1/a^n
must be rational.I will post the solution in higher secondary section.
must be rational.I will post the solution in higher secondary section.
- Sun Feb 13, 2011 11:06 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Secondary 2011/10
- Replies: 7
- Views: 5913
Re: BdMO National Secondary 2011/10
You are not correct.Think more carefully.
- Sun Feb 13, 2011 11:04 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Secondary (Higher Secondary) 2011/7
- Replies: 8
- Views: 6761
Re: BdMO National Secondary (Higher Secondary) 2011/7
Your solution is right.for more easy thinking Let $n=x+y$ where all the members of $x$ are friend to each other.And also all the members of $y$ friend to each other.So any members of $x$ is enemy with any members of $y$. We have also that the number of friendship and enmity is equal. $\displaystyle ...