Evaluate frac 2 6-5 sqrt 3 - JAMB Mathematics 2006 Question
Evaluate (\frac{2}{6-5\sqrt{3}})
A
\(-\left(\frac{12}{39}-\frac{10\sqrt{3}}{39}\right)\)
B
\(\frac{12}{39}-\frac{10\sqrt{3}}{39}\)
C
\(-\left(\frac{12}{39}+\frac{10\sqrt{3}}{39}\right)\)
D
\(\frac{12}{39}+\frac{10\sqrt{3}}{39}\)
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Correct Option: C
(\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}\
=-\left(\frac{12}{39}-\frac{10\sqrt{3}}{39}\right))
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