Evaluate (frac{2}{6-5sqrt{3}})
- A.
(-left(frac{12}{39}-frac{10sqrt{3}}{39}right)) - B.
(frac{12}{39}-frac{10sqrt{3}}{39}) - C.
(-left(frac{12}{39}+frac{10sqrt{3}}{39}right)) - D.
(frac{12}{39}+frac{10sqrt{3}}{39})
Correct Answer: Option A
Explanation
(frac{2}{6-5sqrt{3}} = frac{2}{6-5sqrt{3}} times frac{6+5sqrt{3}}{6+5sqrt{3}}\
=frac{2(6+5sqrt{3})}{(6-5sqrt{3})(6+5sqrt{3})}\
=frac{12+10-sqrt{3}}{36-25(3)}\
=frac{12+10-sqrt{3}}{36-75}\
=frac{12+10-sqrt{3}}{-39}\
=-left(frac{12}{39}-frac{10sqrt{3}}{39}right))