\(\text{The equation $x^2+ ax = -14$ has only integer solutions for $x$. If $a$ is a positive integer, what is the greatest possible value of $a$? }\)
\(\text{The equation $x^2+ ax = -14$ has only integer solutions for $x$.}\\ \text{ If $a$ is a positive integer, what is the greatest possible value of $a$?}\)
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 ?
\(\color{BrickRed}x^2+ax+14=0\\ x=-\frac{a}{2}\pm\sqrt{(\frac{a}{2})^2-14}\)
\(a\in \mathbb{N^{odd}}\ |\ \{[(\frac{a}{2})^2-14]\} \subset\{squares\}\)
\(a\in \{9;15\}\)
\(x^2+ax+14=0\)
\(a=9;\ x_1=-2;\ x_2=-7\\ a=15;\ x_1=-1;\ x_2=-14 \)
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