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
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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.
Source: Myschool Past Questions Archive (Record #22)