The sum of the squares of three consecutive positive integers is 245. What are the integers?
Hello, blame_canada100!
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: .$\displaystyle 8,\:9,\:10$