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