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Find the values of m and n respectively

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})