Question

Consider the pair of equations: $x^2 - xy - x = 22$ and $y^2 - xy + y = 34$. If x > y, then x- y equals

• A. 8
• B. 6
• C. 7
• D. 4

Answer 1

Answer: (A)

8

Answer 2

Given:$x^2-xy-x=22$ and $y^2-xy+y=34$
Adding the two given equations we get:
$x^2-2xy+y^2-x+y=56$
$⇒ (x-y)^2-(x-y)=56$

Let $(x-y) =t$
$⇒ t^2-t=56$
$t^2-t-56=0$
$(t-8)(t+7) =0$
so $t=8$
so $x-y =8$