Find three even consecutive integers such that the sum of the squares of the first and second integers is equal to the square of the third integer plus 20.

Answer 1

If n is a number, a way to ensure we are specifying an even number is to multiply it by 2 (call it 2n)

So the three consecutive numbers are 2n, 2n + 2, and 2n + 4.

So: (2n)² + (2n + 2)² = (2n + 4)² + 20

4n² + 4n² + 8n + 4 = 4n² + 16n +16 + 20

4n² - 8n -32 = 0

n² - 2n - 8 = 0

(n + 2)(n - 4) = 0

n = -2 or 4

therefore, plugging these values of n into "2n", we get two possible answers: -4, -2, 0 and 8, 10, 12