Question

If \(\frac{2}{\sqrt{x}} = 2\) and \(\frac{4}{\sqrt{y}} = -1\), then

• A. \(x = 4\), \(y = 3\)
• B. \(x = 2\), \(y = 9\)
• C. \(x = 4\), \(y = 9\)
• D. \(x = 2\), \(y = 3\)

Hint:

When solving for variables under square roots, isolate the square root term and square both sides to eliminate the square root.

Answer 1

The Correct Option is C

For the first equation \(\frac{2}{\sqrt{x}} = 2\), squaring both sides gives: \[ \sqrt{x} = 1 \quad \Rightarrow \quad x = 4 \] For the second equation \(\frac{4}{\sqrt{y}} = -1\), squaring both sides gives: \[ \sqrt{y} = -4 \quad \Rightarrow \quad y = 9 \] Thus, the correct answer is \(x = 4\) and \(y = 9\).