An Easy Hack to Solve This Radical Math Challenge | Algebra

An Easy Hack to Solve This Radical Math Challenge | Algebra
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In this video, we explore an algebra challenge from 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.
📣 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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[@Fjfurufjdfjd]

χ=1+(3)^(1/2)

[@RashmiRay-c1y]

Note that [7/3+4/(√3)]^1/2= (2+√3)/(√3). Thus, E= [44√3 +76]^1/5. Let x^5=44√3 +76 and y^5 = 44√3 -76. Then, xy=2 and x^5-y^5=152. Let x-y=a. So, a satisfies a^5+10a^3+20a-152=0 which implies a=x-y=2. So, x-2/x=2 which gives x =E=√3 +1.

[@gregevgeni1864]

1+√3

[@RealQinnMalloryu4]

x^5+{10+10 ➖ }+{66+66 ➖ }{7+7 ➖ }/{3+3 ➖ }+{4+4 ➖ }/{3+3 ➖ }=x^5{20+132}{14/6+8/6}=x^5 {152+22}/6={x^5*174}/6=174x^5/6=29x^5 29^1x^5 1^1x^2^3 x^2^3 (x ➖ 3x+2).

[@ruizhong9669]

1+ √3