Jambmaths question:
Rationalize $\frac{2}{6-5\sqrt{3}}$
Option A:
$-\tfrac{12}{39}-\tfrac{10\sqrt{3}}{39}$
Option B:
$\tfrac{12}{39}-\tfrac{10\sqrt{3}}{39}$
Option C:
$-\tfrac{12}{39}+\tfrac{10\sqrt{3}}{39}$
Option D:
$\tfrac{12}{39}+\tfrac{10\sqrt{3}}{39}$
Jamb Maths Solution:
$\begin{align} & \frac{2}{6-5\sqrt{3}}=\frac{2}{6-5\sqrt{3}}\times \frac{6+5\sqrt{3}}{6+5\sqrt{3}} \\ & =\frac{2(6+5\sqrt{3)}}{36-75}=\frac{2(6+5\sqrt{3})}{-39} \\ & =-\frac{12}{39}-\frac{10\sqrt{3}}{39} \end{align}$
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