JAMB 1999 · UME · Q17

Quadratics & their graphs

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

Worked solution (try it first)

Write the integers as $k$ , $k + 1$ and $k + 2$ .
Then $(k + 1)^2 = 3(2k + 2)$ .
Expand: $k^2 + 2k + 1 = 6k + 6$ , so $k^2 - 4k - 5 = 0$ .
Factorise: $(k - 5)(k + 1) = 0$ .
The integers are positive, so $k = 5$ .
So $m = k + 2 = 7$ , option D.

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