Search found 21 matches
- Sun Nov 06, 2011 9:32 pm
- Forum: National Math Camp
- Topic: Exercise-1.15(new book) (BOMC-2011)
- Replies: 10
- Views: 7944
Re: Exercise-1.15(new book) (BOMC-2011)
I wanted to prove each of the fractions be less than or equal to \[1/3\] WLOG let \[a\geq b\Rightarrow a/b\geq 1\] so,\[ab/\left ( b^5\left ( 1+\left ( a^5/b^5 \right ) \right ) +ab\right )\leq ab/\left ( 2b^5+ab \right )=a/\left ( a+2b^4 \right )\] which is \[\leq 1/3\] for any positive integer.I c...
- Sun Nov 06, 2011 6:26 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Problems Involving Triangles
- Replies: 8
- Views: 5744
Re: Problems Involving Triangles
opps. let M be any arbitrary point INSIDE the triangle
- Sun Nov 06, 2011 6:23 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Problems Involving Triangles
- Replies: 8
- Views: 5744
Re: Problems Involving Triangles
\[MA+MB> AB ,MB+MC>BC, MC+MA>CA\]
Add the three inequalities and get the desired result.
Let \[M\]
be any arbitrary point on \[\Delta ABC\]
notice \[MA\]
has to be smaller than any of the three sides of the triangle. The rest is ur's to solve
Add the three inequalities and get the desired result.
Let \[M\]
be any arbitrary point on \[\Delta ABC\]
notice \[MA\]
has to be smaller than any of the three sides of the triangle. The rest is ur's to solve
- Fri Nov 04, 2011 10:34 am
- Forum: H. Secondary: Solved
- Topic: Rangpur Higher Secondary 2011/7
- Replies: 14
- Views: 19303
Re: Rangpur Higher Secondary 2011/7
ans is -13.
- Thu Nov 03, 2011 7:43 pm
- Forum: National Math Camp
- Topic: From the Mayhem. (Again)
- Replies: 4
- Views: 3332
From the Mayhem. (Again)
Let\[\left \lfloor x \right \rfloor\]be the greatest integer not exceeding\[x\] and let\[\left \{ x \right \}\]be the fractional part of the real number\[x\]. Find all positive real number\[x\] such that\[\left \{ \left (2x+3 \right )/\left (x+2 \right ) \right \} + \left \lfloor \left ( 2x+1 \right...
- Thu Nov 03, 2011 7:28 pm
- Forum: National Math Camp
- Topic: From the Mayhem.
- Replies: 2
- Views: 2500
From the Mayhem.
Find all pairs of real number \[\left ( x,y \right )\]
such that\[x^2+(y^2-y-2)^2=0\]
such that\[x^2+(y^2-y-2)^2=0\]
- Thu Nov 03, 2011 7:21 pm
- Forum: Site Support
- Topic: How to use LaTeX
- Replies: 68
- Views: 1382449
Re: How to use LaTeX
\[abc(a+b+c)\leqslant a^3b+b^3c+c^3a\]
yahoo. shikhe gesi....
yahoo. shikhe gesi....
- Wed Oct 19, 2011 1:01 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2009/5
- Replies: 5
- Views: 4549
Re: BdMO National Higher Secondary 2009/5
I think the answer is 2. P is the incenter of ABC. Can somebody please post the proof?? I am missing the easier solution and keeping messing around with many things. Proved a lot of unnecessary contents.
- Wed Oct 19, 2011 12:06 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2009/2
- Replies: 3
- Views: 8915
Re: BdMO National Higher Secondary 2009/2
(x,y) = (4,-5), (-4,-5), (3,2), (-3,2), (2,-1), (-2,-1)
- Wed Oct 19, 2011 12:02 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2009/4
- Replies: 3
- Views: 3424
Re: BdMO National Higher Secondary 2009/4
AM, BM ,CM are the locus of p that satisfies the given inequality. the proof is very trivial.....