Question 9

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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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