Question 8

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Jambmaths question: 

Rationalize $\frac{2-\sqrt{5}}{3-\sqrt{5}}$

Option A: 

$\frac{\sqrt{5}-1}{2}$

Option B: 

$\frac{1+\sqrt{5}}{4}$

Option C: 

$\frac{1-\sqrt{5}}{4}$

Option D: 

$\frac{1-\sqrt{5}}{2}$

Jamb Maths Solution: 

Note: You can either rationalize the numerator or the denominator, but from the option given, it was denominator that was rationalized. So determine the conjugate of $3+\sqrt{5}$\[\begin{align}  & \frac{2-\sqrt{5}}{3-\sqrt{5}}=\frac{2-\sqrt{5}}{3-\sqrt{5}}\times \frac{3+\sqrt{5}}{3+\sqrt{5}} \\ & =\frac{6-3\sqrt{5}+2\sqrt{5}-5}{{{3}^{2}}-5}=\frac{1-\sqrt{5}}{4} \\\end{align}\]

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