2006

Mathematics

67ca00ce0c643c71d77dee1f

Evaluate 2/(6-5√3)

A.

-(12/39-(10√3)/39)

B.

12/39-(10√3)/39

C.

-(12/39+(10√3)/39)

D.

12/39+(10√3)/39

Correct Answer: -(12/39+(10√3)/39)

Explanation

SOLUTION : $\frac{2}{6 - 5 \sqrt{3}} = \frac{2}{6 - 5 \sqrt{3}} \times \frac{6 + 5 \sqrt{3}}{6 + 5 \sqrt{3}} = \frac{2 (6 + 5 \sqrt{3})}{(6 - 5 \sqrt{3}) (6 + 5 \sqrt{3})} = \frac{12 + 10 - \sqrt{3}}{36 - 25 (3)} = \frac{12 + 10 - \sqrt{3}}{36 - 75} = \frac{12 + 10 - \sqrt{3}}{- 39} = - (\frac{12}{39} - \frac{10 \sqrt{3}}{39})$

SOLUTION :

\frac{2}{6 - 5 \sqrt{3}} = \frac{2}{6 - 5 \sqrt{3}} \times \frac{6 + 5 \sqrt{3}}{6 + 5 \sqrt{3}} = \frac{2 (6 + 5 \sqrt{3})}{(6 - 5 \sqrt{3}) (6 + 5 \sqrt{3})} = \frac{12 + 10 - \sqrt{3}}{36 - 25 (3)} = \frac{12 + 10 - \sqrt{3}}{36 - 75} = \frac{12 + 10 - \sqrt{3}}{- 39} = - (\frac{12}{39} - \frac{10 \sqrt{3}}{39})

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