Dhaka Higher Secondary 2011/4

Problem for Higher Secondary Group from Divisional Mathematical Olympiad will be solved here.
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BdMO
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Dhaka Higher Secondary 2011/4

Unread post by BdMO » Fri Jan 28, 2011 10:27 pm

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

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leonardo shawon
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Re: Dhaka Higher Secondary 2011/4

Unread post by leonardo shawon » Sat Jan 29, 2011 12:22 pm

what does form mean... Anyone please explain...
Ibtehaz Shawon
BRAC University.

long way to go .....

HandaramTheGreat
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Re: Dhaka Higher Secondary 2011/4

Unread post by HandaramTheGreat » Sat Jan 29, 2011 1:59 pm

\[ a+b+c+d+e=1 \] \[b+c+d+e=1-a \]

if we add all the 5 equations, we'll get
\[ 5a+4(b+c+d+e)=15 \] \[ 5a+4(1-a)=15 \] \[ \therefore a=11 \]

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leonardo shawon
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Re: Dhaka Higher Secondary 2011/4

Unread post by leonardo shawon » Sat Jan 29, 2011 4:00 pm

i found different answers.....

$a+b+c+d+e=1$ its equation 1.

$a-b+c+d+e=2$ from equation 1 $ a+c+d+e=1-b$ so $b=-1/2$
by doing same in each equation, i have got $a=6$ b=-0.5 c=-1 d=-1.5 and e=-2

if im wrong, please give the correct sollution and whats the meaning question. Somebody please make it clear to me. ! ! !
Ibtehaz Shawon
BRAC University.

long way to go .....

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Tahmid Hasan
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Re: Dhaka Higher Secondary 2011/4

Unread post by Tahmid Hasan » Sat Jan 29, 2011 6:25 pm

i also came up with 11 :ugeek:
Last edited by Tahmid Hasan on Sun Jan 30, 2011 10:30 pm, edited 1 time in total.
বড় ভালবাসি তোমায়,মা

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leonardo shawon
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Re: Dhaka Higher Secondary 2011/4

Unread post by leonardo shawon » Sat Jan 29, 2011 8:17 pm

HandaramTheGreat wrote:\[ a+b+c+d+e=1 \] \[b+c+d+e=1-a \]

if we add all the 5 equations, we'll get
\[ 5a+4(b+c+d+e)=15 \] \[ 5a+4(1-a)=15 \] \[ \therefore a=11 \]
bro u made a mistake..

If we add 5 equations, we get
$5a+3(b+c+d+e)=15$
$5a-3a=15-3$
$a=6$
:)
Ibtehaz Shawon
BRAC University.

long way to go .....

HandaramTheGreat
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Re: Dhaka Higher Secondary 2011/4

Unread post by HandaramTheGreat » Sun Jan 30, 2011 10:00 am

:oops: sorry...

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leonardo shawon
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Re: Dhaka Higher Secondary 2011/4

Unread post by leonardo shawon » Sun Jan 30, 2011 11:22 am

its okay Bro... :) dont worry.
Ibtehaz Shawon
BRAC University.

long way to go .....

farhan
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Re: Dhaka Higher Secondary 2011/4

Unread post by farhan » Tue Sep 04, 2012 11:59 am

it was a very easy one....hohoho...bt many got perplexed..

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