The sum of the squares of the three consecutive even natural numbers is 1460. Find the numbers.
Question
Solution 1
Let's denote the three consecutive even natural numbers as n, n+2, and n+4.
The problem states that the sum of the squares of these numbers is 1460. So, we can write the equation as:
n^2 + (n+2)^2 + (n+4)^2 = 1460
Expanding and simplifying this equation gives:
3n^2 + 12n + 20 = 1460
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