What is the value of xy?

SOLUTION

What is the value of \(xy\)?

(1) \(x^2y^2+2xy\pi-3\pi^2 = 0\).

This can be expressed as: \((xy)^2 + 2xy\pi - 3\pi^2 = 0\).

To find the value of \(xy\), we can either directly solve the quadratic for \(xy\) (to simplify, we can denote \(xy\) as \(a\) to get \(a^2 + 2a\pi - 3\pi^2 = 0\) and solve for \(a\)), or factor \((xy)^2 + 2xy\pi - 3\pi^2 = 0\):

\((xy)^2 + 3xy\pi - xy\pi - 3\pi^2 = 0\)

\((xy)(xy + 3\pi) - \pi(xy + 3\pi) = 0\)

\((xy+3\pi)(xy-\pi)=0\)

This gives us two possible solutions: \(xy=-3\pi\) or \(xy=\pi\). This statement is not sufficient to determine a unique solution.

(2) \(xy>-9.5\).

Clearly insufficient.

(1)+(2) From (1), we have two possible values: \(xy = -3\pi \approx -9.45\) and \(xy = \pi \approx 3.14\). Since both values are greater than -9.5, they both satisfy the condition in statement (2). Therefore, even with both statements, we cannot uniquely determine the value of \(xy\). Not sufficient.


Answer: E

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