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    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.
    A 2133 Correct Answer Incorrect Answer
    B 1216 Correct Answer Incorrect Answer
    C 1468 Correct Answer Incorrect Answer
    D None of the above Correct Answer Incorrect Answer

    Solution

    Let, the two numbers be 'a' and 'b', such that, a > b.

    ATQ,

    a2 + b2 = 250

    a - b = 4

    (a - b) 2 = a2 + b2 + 2 X a X b

    Or, 42 = 250 + 2 X a X b

    Or, 2 X a X b = 250 - 16 = 234

    Or, a X b = 117

    a3 - b3 = (a - b) X (a2 + b2 + ab)

    Or, a3 - b3 = 4 X (250 + 117) = 4 X 367 = 1,468

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