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For what values of $k$ given below is  $\dfrac{(k + 2)^2}{(k - 3)}$ an integer?

1. $4 , 8 , 18$
2. $4 , 10 , 16$
3. $4 , 8 , 28$
4. $8 , 26 , 28$

edited

## 1 Answer

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We'll try and eliminate the wrong options

when K = 4  ==>   $\dfrac{(4 + 2)^2}{(4 - 3)}$ = 36 (integer)

when K = 8  ==>   $\dfrac{(8 + 2)^2}{(8 - 3)}$ = $\dfrac{(100)}{(5)}$ = 20 (integer)

when K = 10  ==>   $\dfrac{(10 + 2)^2}{(10 - 3)}$ = $\dfrac{(144)}{(7)}$ = 20.57 (not an integer)

when K = 16  ==>   $\dfrac{(16 + 2)^2}{(16 - 3)}$ = $\dfrac{(324)}{(13)}$ = 24.92 (not an integer)

when K = 18  ==>   $\dfrac{(18 + 2)^2}{(18 - 3)}$ = $\dfrac{(400)}{(15)}$ = 26.66 (not an integer)

when K = 26  ==>   $\dfrac{(26 + 2)^2}{(26 - 3)}$ = $\dfrac{(784)}{(23)}$ = 34.08 (not an integer)

when K = 28  ==>   $\dfrac{(28 + 2)^2}{(28 - 3)}$ = $\dfrac{(900)}{(25)}$ = 36 (integer)

By Verifying all the options we found out the correct option as C) 4, 8, 28

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