If $x - y + z = 0$, then find the value of $\frac{y^{2}}{2xz}-\frac{x^{2}}{2yz}-\frac{z^{2}}{2xy}$.
Answer & explanation
Correct answer: option 1
If $x - y + z = 0$
$\frac{y^{2}}{2xz}-\frac{x^{2}}{2yz}-\frac{z^{2}}{2xy}$
Let the values of x = z = 1 and y = 2 that will satisfy the equation and put in the find equation,
$\frac{y^{2}}{2xz}-\frac{x^{2}}{2yz}-\frac{z^{2}}{2xy}$
= $\frac{2^{2}}{2 ×1 × 1}-\frac{1^{2}}{2×2 × 1}-\frac{1^{2}}{2×1 × 2}$
= 2 - \(\frac{1}{4}\) - \(\frac{1}{4}\) = $\frac{3}{2}$