the three consecutive positive integers can be written as:

x-1, x, x+1, where x is integer, x-1>0 that is x>1

the sum of the squares of three consecutive positive integers is 194:

(x - 1)^2 + x^2 + (x+1)^2 = 194

by solving we find:

x = 8

click here to see the step by step solution of the equation:

8 - 1 = 7

8 + 1 = 9

the three consecutive positive integers are: 7, 8 and 9.