Dhaka Secondary 2011/4

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
Forum rules
Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

Dhaka Secondary 2011/4

Unread post by BdMO » Fri Jan 28, 2011 9:49 pm

\[\begin{align*}a + b + c + d + e =& 1\\ a - 2b + c -2d + e =& 2\\ a + b -3c + d -3e =& 3\\ -4a + b + c - 4d + e =& 4\\ a -5b + c + d - 5e =& 5\end{align*}\]
উপরের সমীকরণগুলো থেকে $a$ এর মান বের কর।
Find $a$ from the above set of equations.

User avatar
*Mahi*
Posts: 1175
Joined: Wed Dec 29, 2010 12:46 pm
Location: 23.786228,90.354974
Contact:

Re: Dhaka Secondary 2011/4

Unread post by *Mahi* » Sat Jan 29, 2011 10:43 pm

Let us number the equations i,ii,iii......serially .Now by subtracting ii from i we get
$b+d=-1/3$
and subtracting iii from i we get,
$c+e=-1/2$
Now the solution is straightforward,$a=11/6$
Please read Forum Guide and Rules before you post.

Use $L^AT_EX$, It makes our work a lot easier!

Nur Muhammad Shafiullah | Mahi

User avatar
Avik Roy
Posts: 156
Joined: Tue Dec 07, 2010 2:07 am

Re: Dhaka Secondary 2011/4

Unread post by Avik Roy » Tue Feb 01, 2011 1:50 am

good solution Mahi,
even I needed some bigger (but not so bigger) steps to solve it ;)
"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

Post Reply