The sum of the squares of three consecutive even natural numbers equals 1460. What are these numbers?

Explanation

Let the three consecutive even numbers be represented as (2x - 2), 2x, and (2x + 2). Their squares add up to 1460: (2x - 2)^2 + (2x)^2 + (2x + 2)^2 = 1460 Expanding and simplifying: 4x^2 - 8x + 4 + 4x^2 + 4x^2 + 8x + 4 = 1460 Combining like terms: 12x^2 + 8 = 1460 Subtract 8 from both sides: 12x^2 = 1452 Divide by 12: x^2 = 121 Taking positive root (since numbers are natural): x = 11 Therefore, the numbers are: 20, 22, and 24.