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If 1+212 is expressed in the ...

If 1+212 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 answer is 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