An Interesting Homemade Exponential Equation

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PLAYLISTS 🎵 :

[raymondarata]

Because the r.h.s. is sqrt(10)/2, x = 1/2 is a logical possible answer. In your video, you showed that sqrt(10)/2 = sqrt(5/2). Simply set 1 + 1/x = 5/2. Multiply both sides by x and then multiply both sides by 2 to get 2x^2 - 5x + 2 = 0. Solve it by factoring. You get (2x - 1)(x - 2) = 0 so x = 1/2 or 2. You check each answer and find that x = 2 is extraneous and x = 1/2 works! Knowing that the function on the l.h.s. is monotonic, you can be sure that x = 1/2 is the only solution.

[MathOrient]

I appreciate your efforts to make up these equations :)

[vladimirkaplun]

An infinite source of the kitchen made equations. Replace 1/2 with 1/3 and another video is ready.

[vbeckerlima]

What program do you use to make the resolution?

[mcwulf]

That was pretty much guess-and-check. Of course the essential bit is showing it's the only solution.

[carlyet]

nominalise the root to root(5/2). Then x as 1/2 is the trivial [(1/2) + 1/(1/2)]^(1/2)

[hertselcorech]

Thank you! I always enjoy watching your shows. Can you please help me solve:
X squared equals to 2 raised to the X. It should have 3 solutions but I don't know how to solve it.

[ParaNozek]

why (x+1/x)^x only defined when x>0?

[MisterPenguin]

"How do you come up with these equations?"
I like to throw variables, integers, radicals, vincula, parantheses, and irrational numbers into a Nutribullet and then make a video.

is what I'm expecting at the end of this video.

Update: I was wrong.

[MatthisDayer]

donald knuth is crying in the corner right now