CAT 2021 Slot 2 QA Question & Solution
AlgebraHard
Question
Consider the pair of equations: $x^{2}-xy-x=22$ and $y^{2}-xy+y=34$. If $x>y$, then $x-y$ equals
Options
6
4
7
8
Solution
We have :
$x^2-xy-x\ =22\ \ \ \ \ \ \left(1\right)$
And $y^2-xy+y\ =34\ \ \ \ \ \ \left(2\right)$
Adding (1) and (2)
we get $x^2-2xy+y^2-x+y\ =56$
we get $\left(x-y\right)^2-\ \left(x-y\right)\ =56$
Let (x-y) =t
we get $t^2-t=56$
$t^2-t-56=0$
(t-8)(t+7) =0
so t=8
so x-y =8