Question

What must be added in \(\frac{9}{x^2} + 4y^2\) to make it a whole square?

• A. \(6x\)
• B. \(6y\)
• C. \(12x\)
• D. \(12y\)

Hint:

When completing the square, multiply the terms that would create a binomial square.

Answer 1

The Correct Option is C

To make \(\frac{9}{x^2} + 4y^2\) a perfect square, we need to find a term that when added will complete the square. The terms that need to be squared are: \[ \sqrt{\frac{9}{x^2}} = \frac{3}{x}, \quad \sqrt{4y^2} = 2y \] So, to complete the square, we add: \[ 2 \cdot \left(\frac{3}{x} \cdot 2y\right) = \frac{12xy}{x} \] Thus, the correct answer is \(12x\).