Three consecutive positive integers k, l and m are such that l(^2) = 3(k+m). Find…

Three consecutive positive integers k, l and m are such that l(^2) = 3(k+m). Find the value of m.

  • A.
    4
  • B.
    5
  • C.
    6
  • D.
    7
Correct Answer: Option D
Explanation

l(^2) = 3 (k + m)

Since they are consecutive positive numbers, we have

l = k+1, m = k+2.

(to) (k+1)(^2) = 3(k + k + 2)

k(^2) + 2k + 1 = 3(2k + 2)

k(^2) + 2k + 1 = 6k + 6

k(^2) + 2k – 6k + 1 – 6 = 0

k(^2) – 4k – 5 = 0

k(^2) – 5k + k – 5 = 0

k(k – 5) + 1(k – 5) = 0

k = -1 or 5

Since k, l and m are positive, then k = 5.

m = k + 2 = 5 + 2

= 7.

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