The sum of two positive numbers is 51 and their product is 230. The positive difference between them is:
41
Let the two numbers be x and y, with \(x + y = 51\) and \(xy = 230\).
Using the identity \((x-y)^2 = (x+y)^2 - 4xy\), we get \((x-y)^2 = 51^2 - 4 \times 230\).
This gives \((x-y)^2 = 2601 - 920 = 1681\).
So \(x - y = \sqrt{1681} = 41\).
Hence, the positive difference between the numbers is 41.
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