Dhaka Secondary 2011/4

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
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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.

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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
and subtracting iii from i we get,
Now the solution is straightforward,$a=11/6$
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Avik Roy
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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 ;)
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