UPSC CDS 2 2022 Math Paper

Let the number be 2
Since p is the difference between a number and its reciprocal
⇒2−1∕2=3∕2=p
⇒p4+4p2=p2(p2+4)=(9∕4)[9∕4+4]
⇒p4+4p2=225∕16
Since q is the difference between the square of the same number and the square of its reciprocal
⇒(2)2−(1∕2)2=15∕4=q
⇒q2=225∕16
∴ The required value is q2