# Math Help - sum of intergers

1. ## sum of intergers

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

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...

3. x
X + 1
x + 2

3x + 3 = 245

ps
I second wat Moo said

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

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

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

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

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

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

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

5. 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

6. Ohh thats right! I didnt read the squares part.

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