Question 207613
Let x, x+1 & x+2 be the three numbers.
x(x+1)+52=(x+2)^2
x^2+x+52=x^2+4x+4
x^2-x^2-4x+x=4-52
-3x=-48
x=-48/-3
x=16 ans. for the smallest number
16=1=17 ans. for the middle number
16+2=18 ans. for the largest number
Proof
16*17+52=18^2
272+52=324
324=324