Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{yz}+\frac{y^2}{xz}+\frac{z^2}{xy}$?
Option 1: $0$
Option 2: $\frac{1}{3}$
Option 3: $1$
Option 4: $3$
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Correct Answer: $3$
Solution :
Given:
$x+y+z=0$
So, $x^3+y^3+z^3=3xyz$
$\frac{x^2}{yz}+\frac{y^2}{xz}+\frac{z^2}{xy}$
= $\frac{x^3}{xyz}+\frac{y^3}{xyz}+\frac{z^3}{xyz}$
= $\frac{x^3+y^3+z^3}{xyz}$
= $\frac{3xyz}{xyz}$
= $3$
Hence, the correct answer is $3$.
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