If l + m + n = 0, then what will be the value of ((l²)/mn+(m²)/nl+(n²)/lm) ?

If l + m + n = 0, then what will be the value of…

If l + m + n = 0, then what will be the value of $(\frac{l^2}{mn}+\frac{m^2}{nl}+\frac{n^2}{lm})$ ?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 3.

If l + m + n = 0, then l³ + m³ + n³ = 3lmn

Now, $(\frac{l^2}{mn}+\frac{m^2}{nl}+\frac{n^2}{lm})$ = [(l³ + m³ + n³)/(lmn)]

= (3lmn)/(lmn)

= 3

Therefore, the value of the expression is 3.