GATE Electrical 2026 | GA | Question: 10

Question

$P$ and $Q$ are two positive integers such that $P^{2}=Q^{2}+13$.

The product of the numbers $P$ and $Q$ is $\_\_\_\_$

• A. $13$
• B. $26$
• C. $39$
• D. $42$

Answer 1

Givewn  P^2 =   Q^2  + 13

P^2  - Q^2 = 13

(P+Q ) (P  - Q ) = 13 *1

From here P + Q = 13  and P - Q

By hit and trail  

P = 7  and Q = 6

(7 + 6 ) * (7 - 6 ) = 13 * 1

P * Q =  7 * 6 = 42

So option D is correct .