Mathematics

If (frac{1+sqrt{2}}{1-sqrt{2}}) is expressed in the form of x+y√2 find the values of x and…

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 Answer: Option A
Explanation

(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+2sqrt{2}}{-1}\
=-3-2sqrt{2}\
∴X and Y = -3 and -2)