Simplify (frac{1 – 2sqrt{5}}{2 + 3sqrt{2}}).
-
A.
(14(2sqrt{2} + 6sqrt{5} – 4sqrt{10})) -
B.
(frac{1}{14}(2 – 3sqrt{2} – 4sqrt{5} – 6sqrt{10})) -
C.
(frac{1}{14}(3sqrt{2} + 4sqrt{5} – 6sqrt{10} – 2)) -
D.
(14(2 + 3sqrt{2} – 6sqrt{5} + 4sqrt{10}))
Correct Answer: Option C
Explanation
(frac{1 – 2sqrt{5}}{2 + 3sqrt{2}} = (frac{1 – 2sqrt{5}}{2 + 3sqrt{2}})(frac{2 – 3sqrt{2}}{2 – 3sqrt{2}}))
= (frac{2 – 3sqrt{2} – 4sqrt{5} + 6sqrt{10}}{4 – 6sqrt{2} + 6sqrt{2} – 18})
= (frac{2 – 3sqrt{2} – 4sqrt{5} + 6sqrt{10}}{-14})
= (frac{1}{14}(3sqrt{2} + 4sqrt{5} – 2 – 6sqrt{10})) (dividing through with the minus sign)