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The sum of three no of …

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The sum of three no of an AP is27 and their product is 405 . Find the number

    • Posted by Rishi Kumar 5 years, 3 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 5 years, 3 months ago

    Let the numbers be a - d, a, a + d which are in AP.

    (a - d) + (a) + (a + d) = 27 .........(1)

    (a - d)(a)(a + d) = 405 ..........(2)

    (1) => 3a = 27

    a = 9

    (2) => (a2 - d2)(a) = 405

    [(9)2 - d2] (9) = 405

    (81 - d2) (9) = 405

    729 - 9d2 = 405

    9d2 = 729 - 405

    9d2 = 324

    d2 = 36

    d = 6

    Now, substitute the values in the 1st equation.

    (a-d) = 9 - 6 = 3

    a = 9

    (a+d) = 9 + 6 = 15

    Hence the numbers are 3, 9 and 15.

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