Question
The sum of the squares of two numbers is 250, and the
difference between the two numbers is 4. Find the absolute difference between the cubes of these two numbers.Solution
Let, the two numbers be 'a' and 'b', such that, a > b.
ATQ,
a2Â + b2Â = 250
a - b = 4
(a - b)Â 2Â = a2Â + b2Â + 2 X a X b
Or, 42Â = 250 + 2 X a X b
Or, 2 X a X b = 250 - 16 = 234
Or, a X b = 117
a3Â - b3Â = (a - b) X (a2Â + b2Â + ab)
Or, a3Â - b3Â = 4 X (250 + 117) = 4 X 367 = 1,468
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