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    Question

    If a 2  + b 2  = 89 and a

    2  - b 2  = 39, then find the value of a 3  - b 3  - 3ab, (a, b >0).
    A 267 Correct Answer Incorrect Answer
    B 271 Correct Answer Incorrect Answer
    C 283 Correct Answer Incorrect Answer
    D 252 Correct Answer Incorrect Answer

    Solution

    a 2  + b 2  = 89 ........ (1)

    a 2  - b 2  = 39 ........ (2)

    From (1) and (2):

    a 2  = 64 => a = 8

    b 2  = 25 => b = 5

    Now,

    a 3  - b 3  - 3ab

    = 8 3  - 5 3  - 3 * 8 * 5 = 512 - 125 – 120 = 267

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