Question

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is​

Answer 1

Given that the product of three consecutive positive integers is 15600 and we have to find the sum of the squares of the integers

As we have two zeroes in 15600 we should have some number ending in zero or in five

156 = 12 × 13

15600 = 12 × 13 × 100 = 12 × 13 × 25 × 4

15600 = 24 × 25 × 26

The product of n (n+1)(n+2) should have a multiple of 5^2

The sum of the squares of these integers 24 , 25 , 26 is

24^2 + 26^2 + 25^2 = 576 + 625 + 676

24^2 + 26^2 + 25^2 = 1877

Answer

1877