A Nice Algebra Challenge | 95% Failed To Solve!

A Nice Algebra Challenge | 95% Failed To Solve!
Welcome to family infyGyan!
In this video, we explore a challenging algebra problem. If you love solving algebraic expressions then this is the perfect challenge for you. Join me as we work through this intricate algebra problem step-by-step. Don't forget to like, comment, and subscribe for more math challenges and solutions!
📌 Topics Covered:
Algebra
Algebraic simplification
Algebraic manipulations
Problem-solving techniques
Reciprocal equation
Algebraic identities
Competitive Math
Math Olympiad
🔢 What You'll Learn:
Strategies for simplifying reciprocal equations
Tips and tricks to approach difficult simplification problems
Step-by-step walkthrough of the solution
🧠 Challenge Yourself:
Pause the video, try to solve the problem on your own, and then watch as we break down the solution. Share your approach and answers in the comments below!
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[@ManojkantSamal]

a=322...May be ^=read as to the power *=read as square root Let 1/x=R So, XR=x(1/x)=1....eqn1 (X^3)(R^3)=1...eqn2 (X^6)(R^6)=1.....eqn3 (X^18)(R^18)=1.....eqn4 As per question X+R=3 Take the cube X^3+R^3+{3xR(x+R)=3^3 X^3+R^3+(3×1×3)=27 X^3+R^3+9=27 X^3+R^3=27-9=18....eqn5 Take the square of eqn5 X^6+R^6+{2×x^3×R^3}=18^2 X^6+R^6+(2×1)=324 X^6+R^6=324-2=322....eqn6 Take the cube of eqn6 X^18+R^18+{3×x^18×R^18(x^6+R^6)=322^3 So, X^18+R^18+(3×1×322)=322^3 X^18 +R^18=(322^3)-(3×322) As per question X^18+R^18=a(a^2-3) So, (322^3)-(3×322)=a^3 -3a So, a=322 Hence a=322

[@AmirgabYT2185]

a=322 🔥

[@Shobhamaths]

a=322👍 x+1/x=3 x^2+1/x^2=7 x^6+1/x^6=343-21=322 (x^6+1/x^6) ^3=322^3 x^18+1/x^18+3*322=(322) ^3 x^18+1/x^18=(322) ^3-3*322 322((322) ^2-3) =a(a^2-3) a=322

[@Quest3669]

X^18+1/x^18= (322)^3-3(222)=a^3-3a hence a=?= 322

[@RashmiRay-c1y]

If a=p+1/p, we see that a(a^2-3)=p^3+1/p^3. If x^18+1/x^18=a(a^2-3), we get p^3+1/p^3=x^18+1/x^18 which implies p= x^(+/-6) and hence a=x^6+1/x^6. But x^3+1/x^3=3(9-3)=18. S0, a-18^2-2 =322.

[@sarantis40kalaitzis48]

What a method! Congratulations❤

[@RashmiRay-c1y]

@@sarantis40kalaitzis48 Thanks!

[@潘博宇-k4l]

a=322.

[@RealQinnMalloryu4]

{x+x ➖}{1+1 ➖}/{x+x ➖}={x^2+2}/x^2=2x^2/x^2=2x^1 (x ➖ 2alx+1){x^18+x^18 ➖}{1+1 ➖}/{x^18+x^18 ➖}={x^36+2}/x^36;=2x^36/x^36=2x^1(x➖ 2x+1). (a^2 ➖ 3)^2=(a^4 ➖ 9)=5 2^3(a ➖ 3a+2).

[@mulla_modi]

you don't need to elaborate upon each single step, people who are watching you already know basic indices rules and addition subtraction, kindly make it brief

[@билал-ж2к]

Я однажды этому автору об этом тоже написал

[@gregevgeni1864]

a = 322 x³+1/x³= =(x+1/x)³-3x•1/x•(x+1/x)=3³-3•3=18. x⁹+1/x⁹ = (x³+1/x³)³-3x³•1/x³•(x³+1/x³) = 18³-3•18=18(18²-3)=18•321. x¹⁸+1/x¹⁸ =(x⁹+1/x⁹)²-2x⁹•1/x⁹ = = (18•321)²-2. So a(a²-3) =(18•321)²-2 => .. . a=322