Cracking an Olympiad Algebra Problem | No Calculator Challenge

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Cracking an Olympiad Algebra Problem | No Calculator Challenge
In this video, we dive into the fascinating world of math Olympiads with a challenging algebra problem that we solve step-by-step-without using a calculator! Join us as we break down the problem, explore various solving techniques, and provide clear explanations to help you master complex algebraic concepts. Whether you're preparing for a math competition or simply love solving difficult problems, this video is perfect for you. Let's crack this Olympiad algebra problem together!
Topics covered:
Math Olympiad
Algebra
Algebraic identities
Algebraic manipulations
Expressions
Simplification
Exponents
Exponent laws/properties/rules
Long division method
Math Tutorial
Problem solving
Olympiad question
Math Olympiad Preparation
Factorization
Timestamps:
0:00 Introduction
0:28 Method-2
0:40 Substitution
1:05 Exponent laws
3:45 Algebraic identities
4:54 Factorization
6:35 Method-2
7:15 Long division
9:08 Method-3
11:10 Answer
#matholympiad #simplification #problemsolving #mathematics #challenge #mathskills #math #algebra #education #expression
📚 Additional Resources:
• Olympiad Simplificatio...
• Radical Simplification...
• Radical Simplification...
• Dual Method for Ration...
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[@woobjun2582]

Thanks a lot for letting me know various ways of simplification, Sir ^.^

[@stepankravchenko3235]

5^15+1

[@user-ny6jf9is3t]

(5^15)+1

[@mohammedsaysrashid3587]

Wonderful introduction clearly explained...

[@RealQuInnMallory]

( x ➖ 3x+2)

[@woobjun2582]

Let t = 5^15,
and the given E = N/D
where
N = t^5 +t +2,
D = t^4 -t^3 +t^2 -t +2.
Then, manipulating N
N = t^5 +t^2 -t^2 -t +2t +2;
N = (t^2)(t^3 +1)
-t(t +1) +2(t+1);
N = (t^2)(t+1)(t^2 -t +1)
-t(t +1) +2(t+1);
N = (t +1)[(t^2)(t^2 -t +1)
-t +2];
N = (t +1)[t^4 -t^3 +t^2
-t +2];
that is,
N = (t +1)[D]
Therefore
E = N/D = (t +1)D/D
= t +1
E = (5^15) +1

[@lawrencehmurcik8905]

If we let N be 5^75 remain and ignore the remainder of N, and if we let D be 5^60 and ignore the remainder of D, then our answer is 5^75/5^60 = 5^15 which is wrong by 1/5^15 OR too small to care -- I am an engineer first and a mathematician second

[@sunil.shegaonkar1]

M. number 1 is excellent.
M. number 2 is easiest.
But in M number 3: what is the basis of choosing (x + 1).

[@infyGyan]

Thanks 🙏.
As method-2 works with division so method-3 should work with multiplication by the same.
Thanks.