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?

Answer 1

Which of the following equations is used in the process of solving this problem?


3n2+ 5 = 116
3n2+ 3n + 3 = 116
3n2+ 6n + 5 = 116

Answer 2

You understand what consecutive means, yes? :)

So let's start by letting an unknown number, `the first of the 3 consecutive numbers`, be called \(\large n\).

That means the next number will be \(\large n+1\).
And the number after that \(\large n+2\).

So these are our 3 consecutive numbers.
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The sum of their SQUARES is 116.
So let's go ahead and write this out.\[\large n^2+(n+1)^2+(n+2)^2=116\]This is how we write out the sum of their squares.
It's the first number squared + the second number squared + the third number squared.

Answer 3

To match one of the forms listed, we'll expand the squares.\[\large n^2+(n^2+n+n+1)+(n^2+2n+2n+4)=116\]If you're confused about how I expanded those out, let me know.
From here, just simplify! :)