Question

The sum of the squares of 3 consecutive positive integers is 116. What are the numbers? Which of the following equations is used in the process of solving this problem?

3n^2 + 5 = 116

3n^2 + 3n + 3 = 116

3n^2 + 6n + 5 = 116

Answer 1

x^2 + (x+1)^2 + (x+2)^2 = 116

so expand the brackets on the LHS of the equals sign, and see which one matches up to your above choices

Answer 2

\[\large x^2 + (x+1)^2 + (x+2)^2 = 116\]
\[\large x^2 + (x+1)(x+1) + (x+2)(x+2) = 116\]
\[\large x^2 + (x^2 + 2x + 1) + (x^2 + 4x + 4) = 116\]
\[\large x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 = 116\]
\[\large 3x^2 + 6x + 5 = 116\]
does this make sense @xo_kansasprincess_xo ?