The sum of two positive numbers is 27 and their product is 170. The positive difference between them is:
7
Let the two numbers be \(a\) and \(b\), with \(a + b = 27\) and \(ab = 170\).
Use the identity \((a - b)^2 = (a + b)^2 - 4ab\).
Substitute the values: \((a - b)^2 = 27^2 - 4 \times 170 = 729 - 680 = 49\).
Take the square root: \(a - b = \sqrt{49} = 7\).
As a check, the numbers are 10 and 17, whose sum is 27 and product is 170.
Hence, the positive difference between the two numbers is 7.
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