An Infinite Radical Expression | The Golden Ratio

🤩 Hello everyone, I'm very excited to bring you a new channel (SyberMath Shorts).
Enjoy...and thank you for your support!!! 🧡🥰🎉🥳🧡

If you need to post a picture of your solution or idea:

#ChallengingMathProblems #Radicals
via @YouTube @Apple @Desmos @NotabilityApp
@googledocs @canva

SIMILAR PROBLEMS 🤩

PLAYLISTS 🎵 :

[SimonClarkstone]

I expected you say that f(x)=√(x²+f(x²)) and somehow proceed from there.

[pellouze]

Not sure how you define this though. If this is the limit of a suite, I assume Un=√x2+√x4+...+√x2n
Problem is, each Un= X*√1+√1+...+√1=X*n which does not even converge
I assume the definition is somehow different?

[coreyyanofsky]

without watching:
define f_n(x) as this expression out to a x^(2^n)
then f_n(x) = (k_n)x where k_1 = 1 and k_n = sqrt(1 + k_{n-1})
k_n converges to the fixed point of sqrt(1 + x) which is phi

[srividhyamoorthy]

Hey! Can you please post some IOQM or IMO questions cuz it would be quite a challenge

[sy]

Thank you for explaining. Judging from the problem, x is a real number. So, if x<0, I think the result is -x [(1+√5)/2] .
(Note: √(x^8)=x^4, √(x^4)=x^2, but √(x^2)=|x| ) Therefore, I guess |x| [(1+√5)/2] is the best answer.
[[[ If the problem requires x≧0, I would be sorry. ]]]

[mystychief]

y=sqrt(x²) gives y=|x|, etc. etc.... So the answer should be y=|x|*phi and NOT y=x*phi.

[mcwulf]

The golden ratio keeps appearing. But I wouldn't have expected it in this solution! 🤔👍😁

[andirijal]

Sirr what the about if you integral this your question !

[SuperMtheory]

If x = 1/2, then the answer would be phi/2, which is cos (36 degrees).