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.

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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