If (frac{(2sqrt{3}-sqrt{2})}{(sqrt{3}+2sqrt{2})} = m +nsqrt{6}), find the values of m and n respectively.
- A.
1, -2 - B.
-2, 1 - C.
(frac{-2}{5}), 1 - D.
2, 3/5
Correct Answer: Option B
Explanation
Rationalize (frac{(2sqrt{3}-sqrt{2})}{(sqrt{3}+2sqrt{2})}) and equate to (m +nsqrt{6}). Such that m = -2, and n = 1.
Use (sqrt{3}-2sqrt{2}) as the conjugate for Rationalization
(frac{(2sqrt{3}-sqrt{2})}{(sqrt{3}+2sqrt{2})}) X (frac{(sqrt{3}-2sqrt{2})}{(sqrt{3}-2sqrt{2})})
(frac{6 – 4sqrt{6} – sqrt{6} + 4}{3 – 2sqrt{6} + 2sqrt{6} – 8})
=(frac{10 – 5sqrt{6}}{-5})
= -2 + (sqrt{6})