Solving 3^x+4^x=5^x 

isn't it an always decreasing function? since a^x → 0 as x → ∞ for 0 < a < 1? the point made in the video still stands (the expression the left side will only be equal to 1 at one point) but yeah

Classic example of finding A SINGULAR solution by guess/intuition and proving the uniqueness of the solution. Pretty satisfying stuff.

That's the most popular Pythagorean triple, so 2 came in my mind the moment I saw the equation 😅

or just use a theorm with a magnificent proof, which this comment is too small to contain

I’m actually curios, but what about complex solutions?

This equation is of the type a^x + b^x = c^x where a, b and c are positive integers. We know that when x=1 and x=0 the equation is false and when x=2 it is true. We know by Fermat's Last Theorem that no triple of integers satisfy this equation for x>2, so 2 must be the only natural solution. (This tells you nothing about negative or non-integer solutions, let alone complex ones, but still interesting imo)

This is a special case of the fermat's last theorem

A trivial proof would be to show that elliptic curves over the rationals can be obtained by a modular form.

We dont have to do all that. By fermat last theorem the only equation of x^z + y^z = n^z is when z

I dont know why I watch this channel I don't even like math the only reason I use it is because I'm a game programmer there is just something about this channel that I can't get enough of

X FROM BFDI HAS NOW FOUND HIS REAL VALUE AND IT ISNT 7. AHHAHAHAHAHA😂

You’re proving Fermat’s last Theorem, good luck, i have a really neat proof for this but it won’t fit in this comments section.

I knew it because of the 3, 4, 5 triangle

3/5 and 4/5 are sins and cosines of something 37... so they add up when squared to unity

Fermat's last theorem

I don't understand, really.

Wheres the "And then we are done!" :(((

日本人ですがこの説明はわかりやすいです！

3^2 + 4^2 = (3×3) + (4×4) = 9 + 16 =25 5^2 = 5×5 = 25 that's cool and all, but I just easily did it without that super complex math

Meanwhile me Ummm we put it in a triangle Dumb me

by Fermat's Last Theorem there cannot be an integer solution for x > 2. Which, in my mind, also negates any other real result. I have a nice proof but the comment section is too small to write it down over here.

I don't get it

Just put in 2 instead of x and you’ll get the answer, although if you had to solve it without knowing the answer you’d have to play a guessing game which in this case is easily doable

If we consider sin x=0.6 so sin x^2= 0.36 & cos x^2 = 1 - sin x^2 = 0.64 so sin x = 0.8 so we can result x=2

Another answer is Fermat's Last Theorem. Hence, 2

Solve this by using AM-GM inequality if both power are same.

You are telling people something that is not correct. That function is decreasing.

You holding the mic is so annoying!!! Otherwise, great job!!!

I’m in 8th grade we were doing Pythagorean theorem and I did this exact equation

Sensei looks great with beard!

Didn’t you just prove Fermat’s Last Theorem?

Pythagorean theorem a squared plus b squared equals c squared

I swear that you upload so much that youtube can't handle it and doesn't send notifications

pythagorean triplets 3 4 5? like dobereiner triada Li Na K

You could use here Pythagorean Triplet

We could have also solved this using Graphs.

We can simply say that it is a Pythagorean triplets

Pythagoras would be proud

9+16=25 is typing...

can we solve it step but step (is possible?)??

Isn't that called pythahoras theorem

I see a squared plus b squared equals c squared

I can't get my eyes off your beard

Like a pythagoric triangle.

How dawg i only see the answer being 0

Also is a triangule pythagorian

It's also a pythagorean triplet

Isn't that the Pythagoras theorem

Here are two other solutions: Move everything to the left part (i. e. subtract the right part) and take the derivative. I think it's easy to finish this solution. According to the description, this is a Pythagorean equation, so x should be an integer. Case x>2 is a corollary of the Fermat theorem, x

Should it be decreasing

Use easy triangle math first

decreasing*

Use fermat last theorem

Pythagorean triple 😎

İsnt that Pisagors theorem

Idk if I'm dumb but i got x=-2

Even a kid knows x = 2 in Asian

This makes zero sense to me!

It was 2 as we know 3,4,5 are Pythagorean triplet

is it not decreasing tho?

Pythagorean triplet

So what is the result?

বুঝিনাই কাগা

Simply use log

Yeah what he said

The most popular Pythagorean triple

Trigonometry

Or say, by Fermat's Last Theorem, there are no solutions after 2. And leave the classroom like a boss

I knew the answer that x=2, because its a pythagoreas triplet. Also i m in high school. So dont judge.

ooooooo

Fermat eq.

Inter

Huh?

Wtf

w a t

Just 3 4 5 are pythagoras number

wat

जय श्री राम 🚩🚩

or just know Pythagorean Theorem and understand that 3 4 5 right angled triangles exist

I just figured it was 2 because I know that 3, 4 and 5 can be sides to a right triangle, from geometry. I didn't understand your explanation at all but I got the right answer using totally unrelated knowledge and that is the story of my life

You can also use fermat’s last theorem too lol

The reason being why this is only 2 is also a connection with the proof of Fermat's Last Theorem, where there are no possible numbers for n (or x in this case) where it could fit the equality statement. Try as you might, it never works.

I'm very interested to understand if is it possible to isolate the x in this case? Could you demonstrate it?

Fermats last theorem QED

It is a always decreasing function. Despite this glits, it is a clear proving.

𓆣𓆡𓆟𓆟

This is a group of number where u can find it in a right triangle

But how do u get 2?

🤩🤩

The most basic Pythagorean Triplet ?!🙂

I know the answer because of the Pythagorean theorem. Lol cuz there is a right triangle with sides of 3 4 5

I just presumed this was gonna be to do with pythagoras theorem

What about complex solutions?

Anybody who knows Pythagoras should know this by now

What about complex solutions

My boy just solved fermat last theorem

that is always an decreasing function

Just use Fermat's Theorem.

I thought of the Pythagoras theorem.So makes sense

Isn’t it a decreasing function?