Question 977116
smallest = m
next number would be = m+1 (because consecutive positive numbers)
largest number = m+2

3*(m+2)^2 = m^2 + (m+1)^2 + 67 (given in ques)
3*(m^2+4+4m) = m^2+ m^2+1+2m +67
3m^2 + 12m + 12 = 2m^2 + 2m + 68
m^2 + 10m - 56 = 0

Simplify   m^2+10m -56 = 0

 m^2 - 4m + 14m - 56 = 0

m(m-4) +14(m-4) = 0

(m-4)(m+14)=0

so the factors are 4 and -14

m cannot be -14 as it is positive integer

so m = 4
and numbers are 4,5,6