CAT 2022

Slot 2

QA

Question & Solution

Case 1: When $x^2-3x-10=0$ and $x^2-10 e 0$

$x^2-3x-10=0$, or, $(x-5)(x+2) = 0$

or, $x=5$ or $x=-2$

Case 2: $x^2-10=1$

$x^2-11=0$

No integer solutions

Case 3: $x^2-10=-1$ and $x^2-3x-10$ is even

$x^2-9=0$

or, $(x+3)(x-3)=0$

or, $x= -3$ and $x=3$

for $x= -3$ and $x=+3$, $x^2-3x-10$ is even

In total 4 values of $x$ satisfy the equations