Скачать или смотреть IMO Algebra Challenge | Prove the Inequality with Real Numbers XYZ | International Math Olympiad

Heavenly Bodhisata! 🌟 Today, Teacher Failank presents a fascinating inequality from the International Mathematical Olympiad (IMO) — the very same problem that Donnie solved in his first year of high school. That year, the Chinese team won gold with a perfect score! 🏅✨

The problem:
👉 Given real numbers x, y, z, all distinct and satisfying xyz = 1, prove that:

(
𝑥
/
(
𝑥
−
1
)
)
2
+
(
𝑦
/
(
𝑦
−
1
)
)
2
+
(
𝑧
/
(
𝑧
−
1
)
)
2
≥
1
(x/(x−1))
2
+(y/(y−1))
2
+(z/(z−1))
2
≥1

In this lecture:
✔️ We break down the problem step by step
✔️ Introduce substitutions to simplify the fractions
✔️ Transform the equation using symmetry
✔️ Show how the inequality holds true by completing the square

Teacher Ark carefully guides the process, turning a seemingly complex inequality into an elegant solution. The key lies in transforming variables into a, b, c to simplify the structure and then proving that the squared sum is always at least 1.

✨ Key Takeaways:

Learn how substitutions reveal hidden symmetry

Understand how to work with conditions like xyz = 1

Discover a creative approach to proving inequalities at the Olympiad level

This problem showcases the beauty of algebra in competition math: taking intimidating structures and breaking them into elegant, manageable parts. 💡

Whether you’re a student preparing for math contests, a teacher looking for fresh examples, or just someone who enjoys the thrill of solving problems, this episode will sharpen your problem-solving toolkit.

Join us on this journey into the world of Olympiad mathematics — and discover that no problem is too difficult with the right perspective!


#IMO #MathOlympiad #AlgebraChallenge #ProblemSolving #MathCompetition #OlympiadPreparation #Inequalities #Mathematics



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