Q) Number of possible value of pair (x, y) such that x+y+xy=12, x+yxy=-12 (A) 1 (B) 2 (C) 0 - Maths - Relations and Functions

Question

Q) Number of possible value of pair (x, y) such that x + y + x y =
1 2 ,   x + y x y = - 1 2
(A) 1
(B) 2
(C) 0
(D) None of these

Aarushi Mishra · Accepted Answer

x+y+xy=12 _______1x+y=12-xyx+yxy=-12 _______212-xyxy=-12Let t=xy12-tt=-121-2tt=-1-2t2+t=-12t2-t-1=02t2-2t+t-1=02tt-1+t-1=0t-12t+1=0t=1 or t=-12xy=1 or xy=-12Case 1:xy=-12x+y-12=12x+y=1y=1-xxy=-12x1-x=-122x=x-1x=-1y=2Case 2:xy=1x+y+1=12x+y=-12y=-12-xxy=-12x-12-x=1x=-x-122x=-12x=-14y=-12-x=-14Two ordered pair of solutions

Q). Number of possible value of pair (x, y) such that x + y + x y = 1 2 , x + y x y = - 1 2 (A) 1 (B) 2 (C) 0 (D) None of these

Q). Number of possible value of pair (x, y) such that $x + y + \frac{x}{y} = \frac{1}{2}, (x + y) \frac{x}{y} = - \frac{1}{2}$
(A) 1
(B) 2
(C) 0
(D) None of these