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    Question

    If 2a + b = 15 and ab = 18, then the value of (4a² - b²)

    .
    A 135 Correct Answer Incorrect Answer
    B 115 Correct Answer Incorrect Answer
    C 125 Correct Answer Incorrect Answer
    D 105 Correct Answer Incorrect Answer

    Solution

    We know that, (x - y)  2  = (x + y)  2  - 4xy

    So, (2a - b)  2  = (2a + b)  2  - 4 X 2ab

    = 15 2  - 8 X 18 = 225 – 144 = 81

    So, we can say that, (2a - b) = - 9, or, 9.

    Since, all the given options are positive, so we will consider the positive value of (2a - b) , as (2a + b) is given positive.

    We know that, x 2  - y 2  = (x + y) X (x - y)

    So, 4a² - b² = (2a)  2  - b 2 = (2a + b) X (2a - b) = 15 X 9 = 135

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