# Consecutive integers

• Apr 22nd 2010, 04:03 AM
Masterthief1324
Consecutive integers
There is a question that asks: Find three consecutive integers such that the sum of their squares is 149?

I chose to represent the consecutive integers as x, x+1, x+2. Another person chose to represent it as x-1, x, x+1. It then becomes:

x^2 + (x+1)^2 + (x+2)^2 = 149

or

(x-1)^2 + (x)^2 + (X+2)^2 = 149

The second method gave 7 or -7 as an answer which does give 149. However, when I plug 7 into my method, it does not work. Why? Is it because my method will find a different 3 consecutive integer that will work?
• Apr 22nd 2010, 04:18 AM
Quote:

Originally Posted by Masterthief1324
There is a question that asks: Find three consecutive integers such that the sum of their squares is 149?

I chose to represent the consecutive integers as x, x+1, x+2. Another person chose to represent it as x-1, x, x+1. It then becomes:

x^2 + (x+1)^2 + (x+2)^2 = 149

or

(x-1)^2 + (x)^2 + (X+2)^2 = 149

The second method gave 7 or -7 as an answer which does give 149. However, when I plug 7 into my method, it does not work. Why? Is it because my method will find a different 3 consecutive integer that will work?

Well yeah.

He found, 6,7,8. If you plug in 7 you get 7,8,9

Try plugging in x=6 into yours

Consider you could also solve... (x-2)^2 + (x-1)^2 + x^2 = 149.

If you set x=7 you get 5^2 + 6^2 + 7^2.

But consider you could also solve... x^2 + (x+1)^2 + (x+2)^2 = 149

If you set x=7 you get 7^2 + 8^2 + 9^2.

Just to make sense of this... x=7 is not a solution as you can interpret it in a few ways.

The solution is 6^2 + 7^2 + 8^2 = 149.

Hence 'x' could be 6,7 or 8 depending on how you set it up.
• Apr 22nd 2010, 04:21 AM
pickslides
Quote:

Originally Posted by Masterthief1324

(x-1)^2 + (x)^2 + (X+2)^2 = 149

These are not consecutive. Did you solve this one separately? You should not use the answer for the first to confirm the second.
• Apr 22nd 2010, 04:41 AM
Wilmer
Quote:

Originally Posted by Masterthief1324
Another person chose to represent it as x-1, x, x+1. It then becomes:
(x-1)^2 + (x)^2 + (X+2)^2 = 149

Correct your typo: (x+2) should be (x+1) ; then you'll be ok (Nerd)