TR-MO-R1 2017 Problem 12

$n$ pozitif bir tam sayı olsun.

$x+y=n$ $xy=n+65$

sisteminin $(x,y)$ gerçel çözümlerinin olması için $n$ ' nin en küçük değeri kaçtır?

A) $21$ B) $19$ C) $18$ D) $17$ E) $16$

Official text Turkish Mathematical Olympiad, first round 2017 official paper, page 7. Quoted with source.

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