Question

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

Answer 1

\[x^2+(x+1)^2+(x+2)^2=2030\]
Solve for x.

Answer 2

Use this as a guide\[x^2+(x+1)^2+(x+2)^2=2030\]

Answer 3

The (x+1) is your answer

Answer 4

You're meant to solve for x first.

Answer 5

oh, yea. Totally!

Answer 6

I'm just saying, that the middle one (x+1) would be the answer

Answer 7

I should have said the (x+1) TERM is your answer

Answer 8

Well let's not get ahead of ourselves. All we need to do first is solve for x. We don't want to mess up things and jump steps here do we?

Answer 9

No, we do NOT want to do that!

Answer 10

@belinda_marie Have you finished expanding/distributing yet? Because it's taking an awfully lot of time for just one step.

Answer 11

Sorry, I finished it. My final result was 26. My only problem was setting up the equation.

Answer 12

Well Done. That's correct. Excellent work. When there are questions like this, read the question and use variables that may guide you to your answer. But overall, it's a very good job that you finished it off.

Answer 13

Thank you so much to the both of you!

Answer 14

Lazy approach if you're good at arithmetic: x^2 + (x+1)^2 + (x+2)^2 = 2030, so the middle term will be roughly 1/3 of 2030. What number squared is about 675? Well, 25 squared is 625, so find 26 squared, and 27 squared and maybe 24 squared and add up 3 in a row.