Bunuel wrote:

If \(xy^2 = 12\) and \(xy = 4\), then x =

A. 1

B. 2

C. \(\sqrt{3}\)

D. \(\frac{2}{3}\)

E. \(\frac{4}{3}\)

Let’s first establish that both x and y must be positive. Since xy^2 = 12, we see that x must be positive. And since xy = 4, we see that y must also be positive.

Dividing the first equation by the second, we have:

y = 3

Substituting y = 3 into the second equation, we have:

x(3) = 4

x = 4/3

Alternate Solution:

Let’s rewrite the first equation as:

x(xy) = 12

We are given that xy = 9, so we can substitute:

x(9) = 12

x = 12/9 = 4/3

Answer: E

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