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The equation x^2 + ax = -14 - 6 - 8x has only integer solutions for x. If a is a positive integer, what is the greatest possible value of a?

 Feb 9, 2021
 #1
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Rearrange as

 

x^2 + (a + 8)x  +  20   =   0

 

Note  that 20  =

4 * 5

2 *10

1 * 20

 

So  

(x + 4) ( x + 5) =  x^2  + 9x  + 20    and  a  =1

(x +2)( x +10)  =x^2  +  12x + 20    and  a   = 4

(x + 20) ( x + 1)  = x^2  +  21x +  20    and  a =  13

 

 

cool cool cool

 Feb 9, 2021

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