Question

The difference of the squares of two positive integers, is 325 and their difference is 5. what are the numbers?

Answer 1

You just told @Tony Nwachukwu that if the difference is 3, it doesn't work.
So, why don't you just follow the same steps here?

Answer 2

a = first number

b = second number

Since their difference = 5

a - b = 5

Add b to both sides

a = 5 + b

Subtract 5 to both sides

a - 5 = b

b = a - 5

The difference of the squares of two positive integers, is 325 means:

a² - b² = 325

Use difference of two squares formula:

a² - b² = ( a + b ) ( a - b )

a² - b² = 325

( a + b ) ( a - b ) = 325

Replace b by:

b = a - 5

in this formula

a² - ( a - 5 )² = 325

Use square of difference formula:

( x - y )² = x² - 2 • x • y + y²

a² - ( a - 5 )² = 325

a² - b² = a² - ( a² - 2 • a • 5 + 5² ) = 325

a² - ( a² - 10 a + 25 ) = 325

a² - a² + 10 a - 25 = 325

10 a - 25 = 325

Add 25 to both sides.

10 a = 350

a = 350 / 10

a = 35

Since b = a - 5

b = 35 - 5

b = 30

The numers are::

35 and 30

Check result:

a² - b² = 35² - 30² = 1225 - 900 = 325

a - b = 35 - 30 = 5