Championing the Rational Equation Challenge | Math Olympiad
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- Опубліковано 18 чер 2024
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Championing the Rational Equation Challenge | Math Olympiad
Join us as we dive deep into the world of Olympiad mathematics, tackling the formidable challenge of rational equations head-on! In this exciting video, we'll explore winning strategies, problem-solving techniques, and expert tips to conquer Olympiad rational equation problems like a true champion. Whether you're a seasoned competitor or just starting your Olympiad journey, this is the ultimate guide to mastering rational equations and rising to the top of the leaderboard. Don't miss out on this exhilarating adventure in mathematical excellence!
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📚 Key Highlights:
Step-by-step breakdown of the solution process
Insights into the unique aspects of the rational equation
Tips and tricks for mastering equation through exponent laws
Application of algebraic identities and manipulations
Timestamps:
0:00 Introduction
0:40 Domain
2:20 Algebraic identities
3:15 Exponent laws
4:00 Substitution
8:36 Solutions
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Thanks for Watching !!
@infyGyan
Extremely wonderful explanation....thanks sir 🙏 for sharing
X=2i,-2i,
No real roots. Complex roots: x=±2i.
Solution:
The domain: x≠±2.
After getting common denominator: (x-2)⁶+(x+2)⁶ = 8(x²+4)³
(x²-4x+4)³+(x²+4x+4)³= (2x²+8)³
We have the equation of the type: a³+b³=(a+b)³ with the solution a=0 or b=0 or a+b=0.
The first two give the roots x=±2 which are out of domain, the third one gives the roots x = ±2i.
x cannot be +/-2. The given equation simplifies to x^6-4x^4-16x^2+64=0 > x^2=-4 > x= +/- 2i. Thus, only imaginary roots are allowed.