Math Olympiad Simplification | 2 Unique Ways

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Math Olympiad Simplification | 2 Unique Ways
Welcome to our Math Olympiad series! In this video, we'll dive into the fascinating world of algebraic simplification, exploring two unique methods to simplify complex expressions. Whether you're preparing for a Math Olympiad or just looking to enhance your math skills, these techniques will help you tackle problems with confidence and creativity. Join us and master the art of simplification with clear explanations and step-by-step examples. Don't forget to like, share, and subscribe for more math tips and tricks!
Topics covered:
Algebra Challenge
Math Skills
Expression
Simplifying Expressions
How to simplify expressions
Math Olympiad
Reciprocal equation
Algebra
Math Tricks
Algebraic identities
Algebraic manipulations
Substitution
Math Olympiad Preparation
Math Tutorial
Timestamps:
0:00 Introduction
0:40 Method-1
3:40 Algebraic identities
4:54 Method-2
8:30 Reciprocal equation
10:02 Evaluating expression
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Thanks for Watching !!
‪@infyGyan‬

[@mohammedsaysrashid3587]

a^2+1/a^2=83 ..... thanks for sharing.....it was a wonderful explanation...

[@abcekkdo3749]

83

[@dorkmania]

From y²-x²=9xy, dividing the equation by xy then square the result
(y/x - x/y)² = 9²
=> y²/x² - 2(y/x)(x/y) + x²/y² = 81
=> x²/y² + y²/x² - 2 = 81
=> x²/y² + y²/x² = 83

[@user-ee7nw2rx9s]

Если к искомой сумме прибавить 2, то получается квадрат суммы взаимно обратных величин то есть
(х/у+у/х)^2-2, пусть у/х=а, то искомая сумма (а+1/а)^2-2
А в первом выражении удобно умножить на х, но х=1/(1/х)
Тогда знаменатель равенства делим на х
2-(1/(у/х)=21/(2+у/х),
но у/х=а
2-1/а=21/(2+а)
(2а-1)/а=21/(а+2)
Уравнение приводится к квадратному и легко решается.