The sum of two positive integers is 60 and their positive difference is 26. What is the positive difference between the squares of the two integers?
Can anyone explain this one to me?
Thinking about how this can help you:
x²-y² = (x-y)(x+y)
1560
Sure! Let's break down the problem step by step to find the solution.
Let's call the two positive integers "x" and "y".
The first piece of information given is that the sum of the two positive integers is 60: x + y = 60.
The second piece of information is that the positive difference between the two integers is 26: x - y = 26.
To find the positive difference between the squares of the two integers, we need to find the value of (x^2 - y^2).
We can factorize the difference of squares formula to simplify it: (x - y)(x + y) = (x^2 - y^2).
We already know that (x - y) = 26 from the second piece of information.
Now, let's substitute this value back into the formula: 26(x + y) = (x^2 - y^2).
We also know that the sum of the two positive integers is 60, so we can substitute that into the equation as well: 26(60) = (x^2 - y^2).
Simplifying, we get: 1560 = (x^2 - y^2).
Now, to find the positive difference between the squares of the two integers, we need to find the value of (x^2 - y^2). Therefore, the answer is 1560.
I hope this explanation helps!