Question

The sum of the squares of three consecutive positive integers is 2030. What is the middle integer?

Answer 1

(n)^2+(n+1)^2+(n+2)^2=2030

Answer 2

26

Answer 3

And how did you come up with 26?

Answer 4

n^2+n^2+2n+1+n^2+4n+4=2030
3n^2+6n+5=2030
3n^2+6n-2025=0
n^2+2n-675=0
(n-25)(n+27)=0

n=25, n=-27 Since it is positive the first number is 25.

The second once is equal to 26 :)

Answer 5

well i used a guess and check method,
i started with \[24^2+25^2+26^2=1877\]
and then tried \[25^2+26^2+27^2=2030\]
which turned out right.