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\(\text{The equation $x^2+ ax = -14$ has only integer solutions for $x$. If $a$ is a positive integer, what is the greatest possible value of $a$? }\)

 Aug 17, 2019
 #1
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\(\text{The equation $x^2+ ax = -14$ has only integer solutions for $x$.}\\ \text{ If $a$ is a positive integer, what is the greatest possible value of $a$?}\)

 

Die Gleichung \( x ^ 2 + ax = -14\)  enthält nur ganzzahlige Lösungen für  x . Wenn  a  eine positive ganze Zahl ist, was ist der größtmögliche Wert von  a ?

 

\(\color{BrickRed}x^2+ax+14=0\\ x=-\frac{a}{2}\pm\sqrt{(\frac{a}{2})^2-14}\)

\(a\in \mathbb{N^{odd}}\ |\ \{[(\frac{a}{2})^2-14]\} \subset\{squares\}\)

 

\(a\in \{9;15\}\)

 

\(x^2+ax+14=0\)

\(a=9;\ x_1=-2;\ x_2=-7\\ a=15;\ x_1=-1;\ x_2=-14 \)

laugh  !

 Aug 18, 2019
edited by asinus  Aug 18, 2019
edited by asinus  Aug 18, 2019
edited by asinus  Aug 18, 2019
edited by asinus  Aug 18, 2019
 #2
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Thank you so much!!!laugh

 Aug 19, 2019

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