How amazing 😍👏🏻

Spent like an hour solving this and i got kind of close? I used trig subs and newton's method to numerically solve a cubic, also rational root to reduce a quartic, i got x≈0.4 but the answer is x≈0.58. Regardless I'm glad i got as far as i did without knowing the "trick" to solve this one and doing it brute forcey

@BukhalovAV

28 күн бұрын

I walked the same way...

Yes you said it :)

Great!

Nice.

"From Russia"😂❤

I also really enjoyed this solution technique. I saw trigonometric substitution used to solve equations with a linear radicand a while back and I wondered why we were not exposed to this technique in school because it is quite elegant.

@SyberMath

27 күн бұрын

That’s why they don’t teach it in schools 😁

😊😊😊👍👍👍

Great problem! I really enjoyed watching the solution) The second Hocus Pocus is called "method of solving triganometric equations by auxiliary angle" (i don't know, if it sounds good, but anyway) and in russian "метод решения триганометрическмх уравнений при помощи вспомогательного угла". It can help you if you have something like this: a * cosx ± b * sinx. You just need to multiple (and divide) by sqrt(a^2 + b^2). So, then you wiill have something like a/... * cosx ±b /... * sinx. And the ✨mathemagic✨ you can replace a/... and b /... by cos theta and sin theta (because (a/...)^2 + (b/...)^2 = 1). After that you will have something like this: sint * cosx ± cost * sinx (sin of sum), or, if you want, you can do cos of sum, and you have only sin(x±t) or cos(x±t) My English isn't enough good, but i think, language of mathematics can be more understandable😅

@SyberMath

27 күн бұрын

Your english is fine! 😊

@SyberMath

27 күн бұрын

Thank you for the info!

problem ½[√(1-x)+1]-x² = x√(1-x²) Multiply by 2. Because we will be squaring both sides, prepare for extraneous roots. √(1-x)+1-2x² = 2x√(1-x²) 1-2x² = 2x√(1-x²)-√(1-x) S.B.S. 8x³-8x+1 = 4(x-1)√(x+1) S.B.S. 64x⁶-128x⁴+80x²-15 = 0 let z = 2x z⁶-8z⁴+20z²-15 = 0 let y = z² y³-8y²+20y-15 = 0 y=3 is a root by R.R.T. (y-3) is a factor: (y-3)y²-5(y-3)y+5(y-3) = 0 (y-3)(y²-5y+5) = 0 y-3 = 0 or y²-5y+5 = 0 But y=3 implies x = ± ½ √3. However, replacing x with ± ½ √3 in the initial equation fails to satisfy it. Therefore the y=3 solution is extraneous. So we have y²-5y+5 = 0 y = ½(5±√5) = z² z = ±√[½(5±√5)] = 2x x = ± ½ √[½(5±√5)] testing of all possibilities results in x = ½ √[½(5-√5)] as the only working solution. The rest are extraneous resulting from the two times I squared both sides. answer x = ½ √[½(5-√5)] = √(√5/2) √[cos(π/5)]

@ronbannon

26 күн бұрын

Thank you. Very helpful.

x=cosθ..√(1-cosθ)+1-2(cosθ)^2=2cosθsinθ..√(1-cosθ)=sin2θ+cos2θ..elevo al quadrato..1-cosθ=1+sin4θ.. .-cosθ=sin4θ..θ=210..-cos210=sin840=sin120(ok)...x=-√3/2

Pronounce is good, but whole russia is one problem for our planet.

@allykid4720

28 күн бұрын

Shut up, you're on the math channel. If Russia is a problem for you, go and try solving that on the battlefield.

@royalplutomathebula5316

28 күн бұрын

We are talking about Maths not politics 🙄

@PoduznyGumowyPrzyjaciel

28 күн бұрын

People like you are a problem for our planet. Brainwashed idiots who can't resist sucking american dicks even in a comment section of a maths video.

@vzaimo

28 күн бұрын

For our planet the first problem is the country, that is proud of it's pseudodemocracy and every second says "In God we trust", although it's the main sinner of the world. Привет от медведя!

@fabiopilnik827

28 күн бұрын

I have nothing against Markov or the Russian language or people who learn calculus from Russian books translated to Spanish (better textbooks are not that easy to find in English).