Math Olympiad Challenge - Algebra Problem | Mathematics

Math Olympiad Challenge - Algebra Problem | Mathematics

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[vacuumcarexpo]

My comment was blocked for some reason.

I'll try to rewrite it as follows：

Let P＝x＋y＋z，Q＝xy＋yz＋zx ＆ R＝xyz，then the given

Considering a cubic equation that has solutions x，y＆ z，the conditions that it has three real solutions are P＝3 or P≦－3／2．

（i）P＝3⇒（x，y，z）＝（1，1，1）



But when P＜－3／2，does it have solutions？

I have no idea what to do in order to prove that it has no other solutions．

[wajeehasamreen]

can you please tell where do you get these questions from?

[KM-omhm]

Подсказка: это на самом деле длинное, просто решите уравнения как обычно.