the two consecutive positive integers can be written as:

x, x+1, where x is integer and x>0

the sum of their squares is 145:

x^2 + (x + 1)^2 = 145

by solving we find:

x = 8

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

x + 1 = 8 + 1 = 9

the two consecutive positive integers are 8 and 9.