Brain stumper

[grayson]

here is my algebraic equation that not even symbolab solver could solve.

The equation says that the x root of x equals 100.  So what does x equal?

Just a brain stumper for ya'll

[Genady]

Too easy. Belongs in this forum: Brain Teasers and Puzzles - Science Forums.

[Ghideon]

5 hours ago, grayson said:

The equation says that the x root of x equals 100.  So what does x equal?

Assuming \(x \in  \mathbb{R}  \) then  \(  \sqrt[x]{x}=100 \) has no solution

[Genady]

3 hours ago, Ghideon said:

Assuming x∈R then  x−−√x=100 has no solution

However, if x is a complex number, there are many solutions. Not exact, though. One seems to be ~ (-0.28+0.46i), if my algebra is not mistaken.

Edited September 10, 2023 by Genady

[joigus]

Good insights, guys. (+1 to both)

 

For @grayson,

Spoiler

 

 

Edited September 10, 2023 by joigus
minor addition

[grayson]

wow! I had no idea there was a relation between complex numbers and this problem! I am not the most profound person at math. I am not an actual mathematician. I just do it for a hobby. I need to learn more about complex numbers. But I am trying to improve my idea. I just recommend that you go over to my other topic "take this with a gain of salt" and help me with that. 

Thank you

[Ghideon]

5 hours ago, Genady said:

if x is a complex number, there are many solutions.

You're right!

(I intentionally avoided complex numbers. From another thread, I noticed that the OP might benefit from understanding the basics before diving into complex solutions.)

[Genady]

17 minutes ago, Ghideon said:

I intentionally avoided complex numbers.

I assumed you did. I wanted to mention them for other readers.

[grayson]

1 minute ago, Genady said:

I assumed you did. I wanted to mention them for other readers.

I need to know more about complex numbers. 

@joigus

I am assuming the equation had something to do with Euler's formula, but Idk

[joigus]

17 hours ago, grayson said:

I need to know more about complex numbers. 

@joigus

I am assuming the equation had something to do with Euler's formula, but Idk

If you don't mind my saying, it looks like you have passion for science, but tend to get too far ahead of yourself. Keep in mind that numbers have been studied for at least 6,000 years now. We don't know everything by any means, and some things we will never know; but chances are that you will gain insight much faster and efficiently if you study what's been conquered so far. Every step of the way you are allowed to take initiative, of course: Can I prove this, what about that?

It's a beautiful voyage with far more unexpected vistas than you can even imagine.