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5 May, 02:04

find three consecutive negative integers such that six times the largest is equal to the twice sum of the two smaller integers.

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  1. 5 May, 03:42
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    The consecutive negative integers are - 3, - 4 and - 5.

    Step-by-step explanation:

    Let the three consecutive negative integers be k, (k-1) and (k - 2)

    Now, according to the question:

    6 (Largest Integer) = 2 (Sum of smaller two Integers)

    or, 6 (k) = 2 ((k-1) + (k-2))

    ⇒ 6k = 2 (2k - 3)

    or, 6k = 4k - 6

    or, 6k - 4k = - 6

    or, 2k = - 6 ⇒ k = - 3

    Hence, the largest negative integer = - 3

    The next two consecutive negative integer are (k-1) and (k-2) = (-3-1) and (-3-2)

    = - 4 and - 5

    Hence, the consecutive negative integers are - 3, - 4 and - 5.
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