Question

While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is

Answer 1

Calculation:

Let the other two numbers be m and n respectively.

Original products of numbers = 37mn

New products of numbers = 73mn

⇒ 73mn - 37mn = 720

⇒ mn = 20

But, Arithmetic mean > geometric mean

⇒ (m² + n²)/2 > mn

⇒ (m² + n²) > 2mn

⇒ (m² + n²) > 2 × 20

∴ minimum possible value of sum of squares of other two numbers is 40.