Question 30022
xy = 2  ----(1)
x^2 + y^2 = 4  ----(2)
Use the standard formula 
(x-y)^2 = x^2+y^2 - 2xy
=4 -2X(2)  using (2) and (1)
=4-4 = 0
(x-y) ^2 = 0
Therefore taking sqrt 
(x-y) = 0 ----(3)
Which means x = y  ----(3)
Putting x=y in (1)
xy = 2
yXy = 2
y^2 = 2
y = +or - root(2)
y = +[root(2)] implies from (3) x also = +[root(2)] 
y = -[root(2)] implies from (3) x also = -[root(2)] 
Answer: x = sqrt2, y = sqrt2 (one set of answers)
x = -sqrt2, y = -sqrt2 (another set of  answers)
And both sets hold (on oral verification itself)