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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