Question 1154151
Find three consecutive positive odd integers such that the sum of their squares is 371.

let n be the first positive odd integer

second will be n+2

Third will be n+4

n^2 +(n+2)^2 +(n+4)^2=371

n^2 +n^2 +4n +4 + n^2 +8n +16=371

3n^2+12n + 20=371

3n^2+12n-351=0

divide by 3

n^2+4n-117=0

(n+13)(n-9)=0

n=-13 Or n=9

but n is positive

Therefore n=9

The numbers are 9,11,13

CHECK

9^2+11^2+13^2=371