The difference of the squares of two positive integers, is 325 and their difference is 5.what are the numbers
Let's assume the two positive integers are x and y, where x > y.
According to the given information, we have two equations:
1. x^2 - y^2 = 325 (Equation 1)
2. x - y = 5 (Equation 2)
To solve this system of equations, we can rearrange Equation 1 as follows:
(x + y)(x - y) = 325
Substituting Equation 2 into the above equation, we have:
(x + y)(5) = 325
x + y = 65
Now we have a system of equations:
1. x - y = 5
2. x + y = 65
Adding these two equations together will give us:
2x = 70
x = 35
Substituting x = 35 into Equation 2:
35 + y = 65
y = 30
Therefore, the two positive integers are 35 and 30.