Mathematics

Evaluate (frac{2}{6-5sqrt{3}})

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))