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 \(\frac{12}{39}+\frac{10\sqrt{3}}{39}\)
jamb 2006mathematics

The correct answer is A. \(-\left(\frac{12}{39}-\frac{10\sqrt{3}}{39}\right)\)

\(\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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