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ashu
Find the value of $mn$ if $m+n=8$ and $m-n=2$
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rriz
$(m+n)^2-(m-n)^2=4mn\\ \text{or, }8^2-2^2=4mn\\ \text{or, }64-4=4mn\\ \text{or, }60=4mn\\ \text{or, }mn=\dfrac{60}{4}\\ \text{or, }mn=15$
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jiju
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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