TR-MO-R1 2024 Problem 27

Birbirinden farklı $x$ , $y$ , $z$ gerçel sayıları,

$\begin{aligned} x^2 + y^2 &= 9x + 7y + 6z \\ y^2 + z^2 &= 7x + 7y + 8z \\ z^2 + x^2 &= 6x + 8y + 8z \end{aligned}$

eşitliklerini sağlıyorsa, $\dfrac{15x^2 + 4y^2}{z^2}$ kaçtır?

a) $4$ b) $5$ c) $6$ d) $7$ e) Hiçbiri

Dataset text TÜBİTAK olympiad set, Matematik_2024_1.Asama_27. Quoted with source.

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