Question 9

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Jambmaths question: 

If $\frac{1+\sqrt{2}}{1-\sqrt{2}}$is expressed in the form $x+y\sqrt{2}$, find the values of x and y

Option A: 

( –3, –2)

Option B: 

(–2, 3)

Option C: 

(3,2)

Option D: 

(2, –3)

Jamb Maths Solution: 

$\begin{align}  & \frac{1+\sqrt{2}}{1-\sqrt{2}}=\frac{1+\sqrt{2}}{1-\sqrt{2}}\times \frac{1+\sqrt{2}}{1+\sqrt{2}} \\ & =\frac{1+2+2\sqrt{2}}{1-2} \\ & =\frac{3+2\sqrt{2}}{-1} \\ & =-3-2\sqrt{2}\text{      (}x,y)=(-3,-2) \end{align}$

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