JAMB - Mathematics (2008 - No. 9)
If \(\frac{1+\sqrt{2}}{1-\sqrt{2}}\) is expressed in the form of x+y√2 find the values of x and y
(-3, -2)
(-2, 3)
(3,2)
(2,-3)
Spiegazione
\(\frac{1+\sqrt{2}}{1-\sqrt{2}} \times \frac{1+\sqrt{2}}{1+\sqrt{2}}\)
= \(\frac{1+(1+\sqrt{2})+\sqrt{2}(1+\sqrt{2})}{1^2 - (\sqrt{2})^2}\)
= \(\frac{(1+\sqrt{2}+\sqrt{2}+2)}{1-2}\)
= \(\frac{3+2\sqrt{2}}{-1}\)
= - 3 - 2\(\sqrt{2}\)
∴ X and Y = -3 and -2
= \(\frac{1+(1+\sqrt{2})+\sqrt{2}(1+\sqrt{2})}{1^2 - (\sqrt{2})^2}\)
= \(\frac{(1+\sqrt{2}+\sqrt{2}+2)}{1-2}\)
= \(\frac{3+2\sqrt{2}}{-1}\)
= - 3 - 2\(\sqrt{2}\)
∴ X and Y = -3 and -2