The difference between two numbers is 5 and their products is 14.Find the difference between their cubes.

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Solution

Let x and y be two numbers, then

$x - y = 5 a n d x y = 14 ∴ x^{3} - y^{3} = (x - y)^{3} + 3 x y (x - y) = (5)^{3} + 3 \times 14 \times 5 = 125 + 210 = 335$

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