Dhaka Secondary 2010/1

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
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Dhaka Secondary 2010/1

Unread post by BdMO » Fri Jan 21, 2011 7:03 pm

Sum of two numbers is $2$ and their product is $3$. Find the sum of the reciprocal of the numbers.
[Hint: Reciprocal of $x$ is $\frac 1x$]

Sudip Deb
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Re: Dhaka Secondary 2010/1

Unread post by Sudip Deb » Tue Jan 25, 2011 7:00 pm

Suppose , the numbers are ( 1 -x ) and (1+ x)
=>(1-x)(1+x) = 3 .
=>1 -x^2 = 3
=>-x^2 = 2
=> x^2 = -2
=> x = root(-2)
so, the numbers are (1-root(-2)) and (1+root(-2)) . Now its so easy .

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Re: Dhaka Secondary 2010/1

Unread post by Moon » Tue Feb 01, 2011 11:37 pm

$a+b=2, ab=3$. Notice $\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}$ :)
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