Question

determine 3 consecutive even integers if the square of the largest integer is 84 less than the sum of the squares of the two smaller integers

Answer 1

let the middle number be x, the previous even be x-2, and the third
consecutive number be x+2
(x^2 + (x-2)^2) - (x+2)^2 = 84
x^2 + x^2 - 4x + 4 - x^2 - 4x - 4 = 84
x^2 - 8x - 84 = 0
(x-14)(x+6) = 0
x = 14 or x = -6

if x = 14, the 3 integers were : 12, 14, and 16
if x = -6, the 3 integers were : -8, -6, -4