The sum of two numbers is 24 and the product of the two is 108. What is the square of their difference?

Question

Two numbers are such that their difference, their sum and their product are in the ratio 1:5:24.
What is the product of these two numbers?

Answer 1

144

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Let the numbers are x and y;
We have:
x + y = 24
xy = 108
The square of the difference is:
(x - y)^2= (x + y)^2 - 4xy = 24^2 - 4*108 = 144