If frac 1 sqrt 2 1- sqrt 2 is expressed in the ... - JAMB Mathematics 2008 Question
If \(\frac{1+\sqrt{2}}{1-\sqrt{2}}\) is expressed in the form of x+y√2 find the values of x and y
A
(-3, -2)
B
(-2, 3)
C
(3,2)
D
(2,-3)
correct option: a
(\frac{1+\sqrt{2}}{1-\sqrt{2}} \times \frac{1+\sqrt{2}}{1+\sqrt{2}}\
=\frac{1+(1+\sqrt{2})+\sqrt{2}(1+\sqrt{2})}{1^2 - (\sqrt{2})^2}\
=\frac{(1+\sqrt{2}+\sqrt{2}+2)}{1-2}\
=\frac{3+2\sqrt{2}}{-1}\
=-3-2\sqrt{2}\
∴X and Y = -3 and -2)
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