Given: \(a^2b^2 = 21 - 4ab\)
Since this looks like a quadratic equation, let's set it equal to zero: \(a^2b^2 + 4ab - 21 = 0\)
Factor to get: \((ab +7)(ab -3) = 0\)

So, EITHER \(ab = -7\) OR \(ab =3\)
If \(\)a and \(b\) are negative, then the product \(ab\) must be positive, which means it must be the case that \(ab =3\)

If \(ab =4\), then \(a = \frac{3}{b}\)
Square both sides to get: \(a^2 = (\frac{3}{b})^2 = \frac{9}{b^2}\)

Answer: E