When Ramanujan gets Bored.

Given is a nonlinear diophantine equation involving radicals that we need to denest. sqrt(x)+y=7 and x+sqrt(y)=11. First investigated by Ramanujan, we use a clever difference of two squares arrangement to factor a number into linear factors, giving us a satisfying solution in the Integers. Enjoy! =D

Help me create more free content! =)

--------------------------------------------------------------------------------
Wanna send me some stuff? lel:

Postfach 11 15
06731 Bitterfeld-Wolfen
Saxony-Anhalt
Germany
--------------------------------------------------------------------------------

[bhaisochakaro]

Fact : Ramanujan never gets bored he just counts till infinity.

[thomy]

Proof by not knowing the rigorous method:
So if x and y are natural, that means both of them must be perfect squares less than 11. Only options are then 1, 4 and 9. By the "proof of the keen eye" we can tell x and y must be 9 and 4 Q.E.D

[adikeezl]

8:39 That part killed me out of laughter

[hughjohnston]

I seem to remember reading about this equation in "the man who knew infinity" (about Ramanujan obv) where a friend of his gave him this problem and Ramanujan quickly noticed that you can easily guess the solution by thinking of small enough perfect squares. He was still a young student at the time.

[Stixch]

It’s sad to see only a few of your subscribers actually watch your videos with such great content!

[HAL-ojjb]

Ramanujan: In the title
100 000 Indians: Allow us to introduce ourselves

Btw I really liked how you incorporated your sponsor into the video, that was so smooth ^^

[yogeshwagh]

What a coincidence
Yesterday only I watched the movie " the man who knew infinity"

[Israel..]

One could make an entire channel just going over Ramanujan's proofs and vibing.

[enigma]

Srinivasa Ramnujan was one of the figures that Influenced me in my early life to pursue a career in computer science.

Despite the restrictions on food, being a stranger in a foreign land, diseases etc., his passion for math shined through.

When we face difficulties in life, it is motivating to think about the difficulties he faced and draw courage and optimism from the sacrifice and example made by Ramanujan.

[regantoogood]

I thought of a fun one to tackle this problem, using the sum of the first N natural numbers. First transform the system by using a = √x and b =√y. Subtract the second equation from the first and you get a^2 - a - (b^2 - b) = 4. Dividing both sides by 2 gives (a^2 - a)/2 - (b^2 - b)/2 = 2, which is the sum of the first a-1 natural numbers, subtract the first b-1 natural numbers. That be a telescoping sum, so we get the sum the natural numbers starting at b + 1 to a - 1 = 2. Then it gets a bit hand wavy, and we can say that 1 + 2 = 3, so that can't be it, so we can try - 1 + 0 + 1 + 2 = 2, which checks out. So we then get b + 1 = - 1 and then a - 1 = 2. Solving and then transforming back, we get x = 9 and y = 4. Ta da!

[capitão_paçoca]

I like how all of this is so simple that it could be taught in schools to enhance creativity.

[IshaaqNewton]

Indian scammers after watching this video:
Maybe we shouldn’t have annoyed Flammy that much.

[PrudentialViews]

0:00 Nice piss in that bottle. I loved the video! Keep up the great work

[sledzik]

When he prounouces "y" as "wa" and "why" as "y"

[phscience]

5:10 I think what you meant was that the integers are a unique factorisation domain (ufd), which means that any element has a factorisation into primes (in the sense of ring theory). You might have confused it with Gauss‘s theorem that the polynomial ring of a ufd is itself a ufd.

[cartersharpnack]

Here is what I thought: since sqrt x+ y is 7, y must be less than 7. Since I assumed both were perfect squares, this means y is either 1 or 4. Assuming it's 1, looking at the second equation that would make nine 10, which is not a perfect square. But if y is 4, that makes x + 2=11. This makes x 9, which is a perfect square. It works in both equations, so x=9, y=4.

[studypurposeonly]

The diagram you have in the background is so beautiful. It just stays the pattern even if you keep zooming forever

[RCSmiths]

Ramanujan is quite the legend. Awesome man!

[sakshamghildiyal]

He was not talking to ghosts he was talking to the godess of learning Namagiri.

[brianblumberg]

8:39 "meaning this case right here can go fuck itself" hahaha. I love this dude