# sum of intergers

• May 9th 2008, 01:12 PM
sum of intergers
The sum of the squares of three consecutive positive integers is 245. What are the integers?
• May 9th 2008, 01:17 PM
Moo
Quote:

The sum of three consecutive positive integers is 245. What are integers?

Hello,

Isn't there a typo ? Are you sure it's 245 ? Because it has to be a multiple of 3...
• May 9th 2008, 01:17 PM
NeedHelp18
x
X + 1
x + 2

3x + 3 = 245

ps
I second wat Moo said
• May 9th 2008, 02:05 PM
Soroban

Quote:

The sum of the squares of three consecutive positive integers is 245.
What are the integers?

The three integers are: .$\displaystyle x,\:x+1,\:x+2$

The sum of their squares is: .$\displaystyle x^2 + (x+1)^2 + (x+2)^2 \:=\:245$

. . which simplifies to: .$\displaystyle 3x^2 + 6x - 240 \:=\:0 \quad\Rightarrow\quad x^2 + 2x - 80\:=\:0$

. . which factors: .$\displaystyle (x - 8)(x+10) \:=\:0$

. . and has the positive root: .$\displaystyle x \,=\,8$

Therefore, the integers are: .$\displaystyle 8,\:9,\:10$

• May 9th 2008, 02:07 PM
o_O
Since we're dealing with integers, the solution x = -10 works as well.

x = -10; x + 1 = -9; x + 2 = - 8

Their squares should sum of to 245 as well
• May 9th 2008, 02:17 PM
NeedHelp18
Ohh thats right! I didnt read the squares part.

O.O... the OP said they are positive integers.