p and q are positive integers and pq+qp=3,, then, p2q2+q2p2=

GATE 2021 PREVIOUS QUESTION PAPER

GENERAL APTITUDE

ELECTRONICE & COMMUNICATION 2021 GATE EXAM 

p and q are positive integers and pq+qp=3,$,$ then, p2q2+q2p2=

 (A) 3 

(B) 9 

(C) 7 

(D) 11

ANSWER : C

Given that ,pq+qp=3$,{\displaystyle \frac{p}{q}}+{\displaystyle \frac{q}{p}}=3$

Now, (pq+qp)2=33${\left({\displaystyle \frac{p}{q}}+{\displaystyle \frac{q}{p}}\right)}^2=3^3$

⟹p2q2+q2p2+2pq⋅qp=9[∵(a+b)2=a2+b2+2ab]

⟹p2q2+q2p2+2=9$⟹{\displaystyle \frac{p^2}{q^2}}+{\displaystyle \frac{q^2}{p^2}}+2=9$

⟹p2q2+q2p2=7