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    Question

    If 2x + 4y - 9 = 0, then find the value of 8x 3

     - 723 + 64y 3  + 216xy.
    A 5 Correct Answer Incorrect Answer
    B 6 Correct Answer Incorrect Answer
    C 8 Correct Answer Incorrect Answer
    D 4 Correct Answer Incorrect Answer

    Solution

    2x + 4y - 9 = 0

    If, a + b - c = 0, then, a 3  + b 3  - c 3  = - 3abc

    So, (2x)  3  + (4y)  3  + ( - 9)  3  = - 3 X (2x) X (4y) X (9)

    Or, 8x 3  + 64y 3  - 729 = - 216xy

    Or, 8x 3  + 64y 3  - 729 + 216xy = 0 ....(i)

    8x 3  - 723 + 64y 3  + 216xy = 8x 3  - 729 + 6 + 64y 3  + 216xy

    Put the value of equation (i) in the above equation, we get,

    8x 3  - 723 + 64y 3  + 216xy = 0 + 6 = 6

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