Find two positive numbers whose difference is 8 and whose product is 1505.

The two positive numbers are 35 and 43.

Step-by-step explanation:

Let the two positive numbers be x and x + 8.

It is given that their product is 1505.

Therefore, x(x + 8) = 1505

x(x + 43) - 35(x + 43) = 0

(x + 43)(x - 35) = 0

x = -43, x = 35

Since, the numbers are positive, x = 35 is only valid.

The other number is x + 8 = 35 + 8 = 43.

Hence, the required positive numbers are 35 and 43.