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13 September, 03:49

The product of three consecutive integers is - 1716. what is the greatest of the three integers?

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  1. 13 September, 04:09
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    -11

    Step-by-step explanation:

    If we call x the least integer, then x + 1 is the next integer, and x + 2 is the greatest integer.

    x (x + 1) (x + 2) = - 1716

    x (x² + 3x + 2) = - 1716

    x³ + 3x² + 2x = - 1716

    x³ + 3x² + 2x + 1716 = 0

    That's not an easy equation to factor. We could use rational root test, but that would take a long time. However, we can narrow down the options logically. The three integers are relatively close together, so if we approximated the product as x³:

    x³ ≈ - 1716

    x ≈ - 11.9

    So let's see if x = - 12 is a solution:

    (-12) ³ + 3 (-12) ² + 2 (-12) + 1716 = 396

    Nope. Let's try x = - 11:

    (-11) ³ + 3 (-11) ² + 2 (-11) + 1716 = 726

    Not that either. Let's go the other direction, x = - 13:

    (-13) ³ + 3 (-13) ² + 2 (-13) + 1716 = 0

    Aha! x = - 13. So x + 1 = - 12, and x + 2 = - 11.

    -11 * - 12 * - 13 = - 1716

    The greatest integer is - 11.
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