cat 2021 Question 3

Question

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

Accepted Answer

We have :

$x^2 - xy - x = 22 \quad (1)$

And $y^2 - xy + y = 34 \quad (2)$

Adding (1) and (2)

we get $x^2 - 2xy + y^2 - x + y = 56$

we get $(x - y)^2 - (x - y) = 56$

Let $(x - y) = t$

we get $t^2 - t = 56$

$t^2 - t - 56 = 0$

$(t - 8)(t + 7) = 0$

so $t = 8$

so $x - y = 8$

Question 3.