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profileashu
asked 2016-04-16 12:46:36 
Find the value of $mn$ if $m+n=8$ and $m-n=2$
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profilerriz
answered 2016-06-12 16:01:20 
$(m+n)^2-(m-n)^2=4mn\\
\text{or, }8^2-2^2=4mn\\
\text{or, }64-4=4mn\\
\text{or, }60=4mn\\
\text{or, }mn=\dfrac{60}{4}\\
\text{or, }mn=15$
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profilejiju
answered 2016-04-19 11:28:48 
Ans: $15$

$(m+n)^2=8^2\\
m^2+n^2+2mn=64~~\cdots(1)$

$(m-n)^2=2^2\\
m^2+n^2-2mn=4~~\cdots(2)$

$(1)-(2)$ =>
$4mn=60\\
mn=15$

Note: since the numbers are small, it is easy to identify values of $m$ and $n$ as $5$ and $3$ and therefore we can directly get the answer as $5×3=15$
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