Question:
If x<0 y>0
[x + y +(x/y)] = (1/2) and (x + y)(x/y) = (-1/2)
Then x and y ?

a)|x| = |y|

b)Integers

c)Both (a & b)

d)None

Solution:
Here let P = x+y and Q = x/y so that
P + Q = 1/2 and PQ = -1/2

Upon solving we get;
P = 1 or -1/2

Q = -1/2 or  1

Case-1 : When P = -1/2 and Q = 1
Then,

x+y = -1/2 and x/y = 1

Solving thses we get;

x = -1/4 and y = -1/4.

Here x<0 but y is negative .So we'll skip this.

Case-2: When P = 1 and Q = -1/2 so that

x+y = 1 and x/y = -1/2

Solving these we get ;

x = -1 and y = 2

Both are integers.

Hence (b) is the answer.