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