Find the value of k if \(\frac{k}{\sqrt{3} + \sqrt{2}}\) = k\(\sqrt{3 – 2}\)
- 3
- 2
- \(\sqrt{3}\)
-
\(\sqrt 2\)
The correct answer is: D
Explanation
\(\frac{k}{\sqrt{3} + \sqrt{2}}\) = k\(\sqrt{3 - 2}\)\(\frac{k}{\sqrt{3} + \sqrt{2}}\) x \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}\)
= k\(\sqrt{3 - 2}\)
= k(\(\sqrt{3} - \sqrt{2}\))
= k\(\sqrt{3 - 2}\)
= k\(\sqrt{3}\) - k\(\sqrt{2}\)
= k\(\sqrt{3 - 2}\)
k2 = \(\sqrt{2}\)
k = \(\frac{2}{\sqrt{2}}\)
= \(\sqrt{2}\)