Jambmaths question:
Simplify $\left( \sqrt{2}+\frac{1}{\sqrt{3}} \right)\left( \sqrt{2}-\frac{1}{\sqrt{3}} \right)$
Option A:
$\frac{5}{2}$
Option B:
$\frac{3}{2}$
Option C:
$\frac{5}{3}$
Option D:
$\frac{7}{3}$
Jamb Maths Solution:
$\begin{align} & \left( \sqrt{2}+\frac{1}{\sqrt{3}} \right)\text{and}\left( \sqrt{2}-\frac{1}{\sqrt{3}} \right)\text{are conjugate surds}.\text{ } \\ & \text{The products of two conjugate is a difference of two square} \\ & \left( \sqrt{a}+\sqrt{b} \right)\left( \sqrt{a}-\sqrt{b} \right)={{\left( \sqrt{a} \right)}^{2}}-{{\left( \sqrt{b} \right)}^{2}} \\ & \left( \sqrt{2}+\frac{1}{\sqrt{3}} \right)\left( \sqrt{2}-\frac{1}{\sqrt{3}} \right)={{\left( \sqrt{2} \right)}^{2}}-{{\left( \frac{1}{\sqrt{3}} \right)}^{2}}=2-\frac{1}{3}=\frac{5}{3} \\\end{align}$
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