Question

If $x+y+z=0$, then $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}$ is

• A. $2\sqrt{3}$
• B. $\sqrt{3}$
• C. $3$
• D. $4\sqrt{3}$

Answer 1

Answer: (C)

$3$

If $x+y+z=0$, then $x^3+y^3+z^3=3x\cdot y\cdot z$
$\therefore$ Given Exp. $=$ $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}$
$=$ $\frac{x^3}{xyz}+\frac{y^3}{zxy}+\frac{z^3}{xyz}$
$=$ $\frac{x^3+y^3+z^3}{x\cdot y\cdot z}$
$=$ $\frac{3x\cdot y\cdot z}{x\cdot y\cdot z}=3$