Question 21

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

Name: If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is
Uploaded: July 3, 2020, 10:13 a.m.
Duration: 1 min 42 s
Description: If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

Solution

$$(x -1)x(x+1) = 15600$$
=> $$x^3 - x= 15600 $$
The nearest cube to 15600 is 15625 = $$25^3$$
We can verify that x = 25 satisfies the equation above.
Hence the three numbers are 24, 25, 26. Sum of their squares = 1877

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