A Tricky Radical Math Challenge | Give It a Try!

A Tricky Radical Math Challenge | Give It a Try!
Welcome to another exciting Math Olympiad challenge! In this video, we solve a fascinating radical equation. Join us as we delve into this intriguing algebraic challenge and explore the elegant solutions. Whether you're a math enthusiast, a student preparing for competitions, or simply love solving problems, this video is for you. Let's solve this together and enhance our problem-solving skills!
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🔍 In this video:
Detailed walkthrough of a challenging algebra problem from the Math Olympiad.
Tips and tricks for solving complex algebraic equations.
Encouragement to enhance your problem-solving skills and mathematical thinking.
📣 Call to Action:
Have a go at the problem yourself before watching the solution!
Share your solutions and approaches in the comments below.
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#algebra #radical #math #mathcompetition #problemsolving #learnmaths #mathematics #matholympiadpreparation
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• A Nice Radical Algebra...
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Thank You for Watching!!

[@gregevgeni1864]

2+(x^5 -992)^1/5 = x
(x^5 - 992)^1/5 = x-2 =y .
Then x^5 - 992 = y^5 and (x-2)^5=y^5
=> (after some algebra)
x^4 - 4 x^3 +8 x^3 - 8x - 96 =0 or
(x+2)(x-4)(x^2 -2x+12)=0 etc . .

[@kassuskassus6263]

Two real solutions x=-2 and x=4

[@tejpalsingh366]

X= 4; -2

[@RashmiRay-c1y]

Ley y=[x^5-992]^1/5. Then x-y=2 and x^5-y^5=992. So, (x^5-y^5)/(x-y) = x^4+y^4+xy(x^2+y^2)+x^2y^2 = [(x-y)^2+2xy]^2+xy[(x-y)^2+2xy] -x^2y^2 = 496. Łęt a=xy. Thus, 4(a+2)^2 +2a(a+2)-a^2=496 > a^2+4a-96=0 > a=8, -12. a=-12 does not yield real values of x. If a=8, x-8/x=2 > x=4, -2.

[@RealQinnMalloryu4]

2+1x^1 ➖ 10^90^2^46 1+ 10^9^10^2^23 2^5^9^2^5^2^23^1 1^1^3^2^2^1^1^1 3^1^2^1 32 (x ➖ 3x+2)

[@9허공]

x^5 - 992 = (x - 2)^5 => x^4 - 4x^3 + 8x^3 - 8x - 96 =0
let x = y + 1 => x^4 - 4x^3 + 8x^3 - 8x - 9 = y*4 + 2y^2 - 99 = (y^2 - 9)(y^2 + 11) = 0
=> y = ± 3 => x = { 4, -2 }

[@潘博宇-k4l]

X1 =-2, X2 =4.

[@MathEducation100M]

Nice video