Find the value of k if \(\frac{k}{\sqrt{3} + \sqrt{2}}\) = k\(\sqrt{3 - 2}\)
A
3
B
2
C
\(\sqrt{3}\)
D
\(\sqrt 2\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{k}{\sqrt{3} + \sqrt{2}}\) = 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(\(\sqrt{3}\) - K\(\sqrt{2}\) ) = K\(\sqrt{3}\) - 2
K\(\sqrt{3}\) - K\(\sqrt{3}\) - K\(\sqrt{2}\) = - 2
- K\(\sqrt{2}\) = - 2
K = \(\frac{- 2}{- \sqrt{2}}\)
K = \(\frac{2}{\sqrt{2}}\) x \(\frac{\sqrt{2}}{\sqrt{2}}\)
K = \(\frac{2\sqrt{2}}{2}\) = \(\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #30643)