The Product of two numbers is 140 and the sum of squares of numbers is 449. Find the sum of both numbers.

Question: The Product of two numbers is 140 and the sum of squares of numbers is 449. Find the sum of both numbers.

Solution:
let the two numbers be P and Q respectively.

P × Q = 140 ……..(1)
P² + Q² = 449 ..…..(2)

We know that,
(P + Q)² = P² + Q² + 2PQ
⇒ (P + Q)² = 449 + 2 × 140
= 449 + 280
= 729

∴ P + Q = √729 = 27