Answer:
The numbers are 5 and 10.
Explanation:
Let x be one of the numbers. We know the other number is 5 more, so that number can be x+5.
We can square the bigger number lile this:
(x + 5)^2
Also we can squared the smaller number, x^2.
They said the difference was 75. Difference means subtracting.
(x+5)^2 - x^2 = 75
square the terms
x^2+10x+25-x^2=75
combine like terms.
10x + 25 = 75
subtract 25
10x = 50
divide by 10
x = 5
So the smaller number is 5 and the larger number
x + 5
= 5 + 5
= 10
The numbers are 5 and 10.
One number is 5 more than the other.
The difference if their squares 10^2 and 5^2 is
10^2 - 5^2
= 100 - 25
= 75
The difference is 75.