A Beautiful Radical Math Challenge | Can You Solve?

A Beautiful Radical Math Challenge | Can You Solve?

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In this video, we explore an algebra problem involving radicals, perfect for those preparing for Olympiads. This problem will enhance the understanding of radical expressions and skills of problem-solving. Watch as we break down the solution step-by-step, providing clear explanations and insights along the way.

If you're a Math Olympiad participant or simply enjoy tackling complex math problems, this video is for you. Make sure to like, subscribe, and hit the notification bell to stay updated with more exciting math challenges. Let's solve this radical algebra problem together!

🔍 In this video:

Detailed walkthrough of a challenging algebra problem.
Tips and tricks for solving complex radical expression.
Encouragement to enhance your problem-solving skills and mathematical thinking.

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[ManojkantSamal]

LHS: *5/5x ( *=read as square root )
=1/*5x
So
(1/*5x)^7=1/125.*5.(x)^7
RHS :
Numerator
*2+*3+*4+*6
=(*2+*3)+*2(*2+*3)
=(*2 +*3)(1+*2)
=(*3+*2)(*2+*1)
Denominator
*2+*3+*1+*2
=(*3+*2)+(*2 +*1)
So the given fraction is
{(*3+*2)(*2 +*1)}/{(*3+*2)+(*2+*1)}
Take the inverse of the

=[{(*3+*2)/{(*3+*2)(*2+*1)}]+
[{(*2+*1)/{(*3+*2)(*2 +*1)}]
Now explain the 1st term
1/(*2+*1)=(*2-*1)/1
Explain the 2nd term
1/(*3+*2)=(*3-*2)/1
The total fraction will be
*2-*1+*3-*2=*3-1
Take its square
(*3-1)^2=3+1-(2.*3)
=4-(2.*3)=2(2-*3)
Again take the square
(4-2.*3)^2=16+12-16.*3

Take the cube of (*3-1)
(*3-1)^3=9.*3-1+3.*3(1-*3)
=9.*3-1+3.*3-9
=12.*3-10...eqn2
Eqn1 ×Eqn2
(28-16.*3)(12.*3-10)
=336.*3-280-576+160.*3

Take the reverse of LHS
125.*5.(X)^7
SO,
125.*5.(X)^7=496.*3-856
125.(X)^7=(496.*3-856)/*5
SO,
625(X)^7=*5(496.*3-856)
=8.*5(62.*3-107) (May be )

[Shobhamaths]

If u simplify and rationalize, then
x=(√3-1) /√5;
5x^2=4-2√3
25x^4=28-16√3;
5√5x^3=6√3-19;
Above two u multiply then 625x^7=328√15-568√5👍

[АндрейПергаев-зн]

Зачем лишние действия по возведению в куб
Возвести ещё раз в квадрат
625х^8=(28-13 sqrt 3)^2
х=(sqrt3 - 1)/sqrt 5
Потом поделить на х
х^7=х^8/х

[RealQinnMalloryu]

{5x+5x ➖ }/{5x+5x ➖ }=10x^2/10x^2 =1x^1 (x ➖ 1x+1).{2x+2x ➖ }+{3x+3x ➖ }{+4x+4x ➖ }+{6x+6x ➖ }/{2x+2x ➖ }+3x+3x ➖}+{1x+1x ➖ }+{2x+2x ➖ 30x^6/16x^6=1.14x^1 .2^7x^1 2^7^1x^1 2^1^1x^1 2x^1 (x ➖ 2x+1).16^16x^7, 4^4^4^4x^7^1 2^2^2^22^2^2^2x^1^1 1^1^1^1^1^1^1^2 1^2(x ➖ 2x+1).

[潘博宇-kl]

X=[(3)^(1/2)-1]/(5)^(1/2)=[(15)^(1/2)-(5)^(1/2)]/5, E=328(15)^(1/2)-568(5)^(1/2).

[RashmiRay-cy]

Let y= √5 x. Then, E = √5 y^7. Now, y = [√1 + √2 +√2 +√3]/[√2 + √3 + √2(√2 + √3)] = [√1 + √2 +√2 +√3] /(√1 + √2)(√2+√3) = 1/(√1 + √2) + 1/(√2+√3) = √2 -1 +√3 -√2 = √3-1. Then y^7 = 328 √3 -568 and E = 328√15 - 568√5 = 0.24, approximately.