Question

If $xy\ne 0$ and $x^2{y}^2-xy=6$, which of the following could be y in terms of x ?
I. $\frac{1}{2x}$
II. $-\frac{2}{x}$
III. $\frac{3}{x}$

• A. I only
• B. II only
• C. I and II only
• D. I and III only
• E. II and III

Answer 1

The correct option is E II and III

Solving the quadratic in y

$x^2{y}^2-xy-6=0$

$\to$ y = $\frac{x+/-\sqrt{x^2+24x^2}}{2x^2}$

$\to$ y = ($x$ +/- $5x$)/(2$x^2$)

y = $\frac{3}{x}$ or y = $\frac{-2}{x}$

Option E.