Question

The sum of the squares of three consecutive positive integers is 2030. What is the middle integer?

Answer 1

let the middle integer be x

the smaller integer is x - 1

the larger is x + 1

so you have an equation

\[(x -1)^2 + x^2 + (x + 1)^2 = 2030\]

distribute, collect like terms and then solve for x