Question

Choose the correct answer from the alternatives given.
If x+y+z=0 then what is the value of $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}$ ?

• A. $(xyz{)}^2$
• B. $x^2+y^2+z^2$
• C. $9$
• D. $3$

Answer 1

The correct option is D $3$

We know that when$x+y+z=0$ then, $x^3+y^3+z^3=3xyz$
$\therefore \frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}=\frac{x^3+y^3+z^3}{xyz}\Rightarrow \frac{3xy}{xyz}=3$