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Question
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Solution
Let the two positive numbers be a and b.
Given difference between them is 5 and sum of squares is 73.
So a - b = 5, a2 + b2 = 73
Squaring on both sides gives
(a - b)2 = 52
a2 + b2 - 2ab = 25
but a2 + b2 = 73
so 2ab = 73 - 25 = 48
ab = 24
So, the product of numbers is 24.
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