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    Question

    The cube of the difference between two given natural

    numbers is 1728, while the product of these two given numbers is 108. Find the positive difference between the cubes of these two given numbers.
    A 4104 Correct Answer Incorrect Answer
    B 5616 Correct Answer Incorrect Answer
    C 2160 Correct Answer Incorrect Answer
    D 5626 Correct Answer Incorrect Answer

    Solution

    1st natural number = x 2nd natural number = y (x - y)3 = 1728 (x - y) = 3√1728 = 12            … (1) squaring both sides   (x - y) ² = 144 x2+y2-2xy =144 x² + y² = 144 + 216 = 360 Now, (x + y) = √ (x² + y² + 2xy) =√ (360 + 216) = √576 = 24   … (2) Now Eq (1) + Eq (2). x-y+x+y =12+24=36 2x =36 x=18 y=6 Now positive difference between the cubes= (18)3-(6)3 =5832-216 =5616.

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