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A Nice Radical Equation | Math Olympiad Prep!
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Күн бұрынA Nice Radical Equation | Math Olympiad Prep!
Welcome to another exciting Math Olympiad prep problem! In this video, we'll tackle a captivating radical equation that will test your problem-solving skills. Join me as we explore this intriguing problem step-by-step and learn some useful techniques for simplifying radical equations. Don’t forget to like, comment, and subscribe for more math challenges and solutions!
Whether you're preparing for a math competition or just love tackling tough problems, this video is for you!
We'll cover:
Key concepts and definitions
Common pitfalls and how to avoid them
Detailed example problems with solutions
Tips and tricks to solve these equations efficiently
#matholympiad #radicalequations #mathpreparation #mathchallenge #problemsolving #mathtutorial #mathskills #mathtips #competitivemaths #algebra #mathematics
Time-stamps:
00:00 Introduction
02:12 Reciprocal Equation
03:50 Substitution
04:18 Algebraic identities
05:15 Solving cubic equation using factorization
07:45 Complex solutions
09:20 Real solutions
Additional Resources:
• A Terrific Radical Equ...
• Nice Algebra Challenge...
• A Nice Radical Equatio...
• A Nice Radical Equatio...
Join us and boost your problem-solving skills to ace the Math Olympiad! Don't forget to like, subscribe, and hit the notification bell for more expert math tips and tutorials.
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@user-kp2rd5qv8g Ай бұрын
Squaring, we get x^6-2x^4-100x^2-2x^2+1=0 > x^3+1/x^3 -2(x+1/x) -100=0. Let x+1/x=t > t^3-5t -100 =0. t=5 is the only real solution. So, x+1/x=5 > x^2-5x+1=0 > x = 1/2[5 +/- sqrt(21)].
@kassuskassus6263 Ай бұрын
Square both sides and let u=x+1/x. We get u^3-5u-100=0. We solve for u and we get only one real solution which is u=5. That gives us x=(5+or-sqrt21)/2.
@user-kt1dm9jz5t Ай бұрын
X=[5+(21)1/2]/2; [5-(21)1/2]/2.
@mohammedsaysrashid3587 Ай бұрын
It was a wonderful explanation. Thank you Sir 🙏 for sharing ...
@infyGyan Ай бұрын
You are most welcome, thanks for watching.
@tejpalsingh366 Ай бұрын
X= (5 + - √21)/2 only real solns. Rest r complex .
@RajeshKumar-wu7ox Ай бұрын
X=((5+√21) /2),((5-√21)/2), comlex root
@ashokdubey8415 Ай бұрын
x can't be complex as RHS>=0 => LHS i.e. x>=0
@RealQinnMalloryu4 Ай бұрын
2x^12/{(2x^2+100x)+2})={(102x^3+2})= 2x^+2/104x^3 = 52x^1.1 2^26x^ 2x^13 2x13^1 2x^1^1 2x^1 (x ➖ 2x+1)
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