Question : If $l+m+n=0$, then what will be the value of $(\frac{l^2}{mn}+\frac{m^2}{nl}+\frac{n^2}{lm})^2$?
Option 1: 9
Option 2: 16
Option 3: 4
Option 4: 1
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Correct Answer: 9
Solution :
Given, $l+m+n=0$
$(\frac{l^2}{mn}+\frac{m^2}{nl}+\frac{n^2}{lm})^2$
$= (\frac{l^3+m^3+n^3}{lmn})^2$
We know, if $l+m+n=0$, then $l^3+m^3+n^3=3lmn$
$= (\frac{3lmn}{lmn})^2$
$= 9$
Hence, the correct answer is 9.
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