Thread: 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?

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.

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.

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