Germany - Math Olympiad Algebra Problem

This is an interesting question with amazing concepts!
Playlist to watch all videos on Learncommunolizer
• Maths Olympiad
And
• Maths
Subscribe: / @learncommunolizer

[@rdeviltron]

CONGRATULATION, bro, for hitting the 100,000 subscribers. You're awesome.

[@learncommunolizer]

Thank you very much 🎉🙏

[@ruddysenseinet3128]

100.000 subs! 👍💯
Congratulations!
Where do you get these algebra olympiads exercises from?

[@cyruschang1904]

a^4 = (a - 1)^4 = a^4 - 4a^3 + 6a^2 - 4a + 1
4a^3 - 6a^2 + 4a - 1 = 0
(2a - 1)(2a^2 - 2a + 1) = 0
a = 1/2, (1 +/- i)/2

[@joseeoliviero6078]

Can you just expand the right side using Pascal's Triangle.... Then work it from there?

[@ΑΝΤΩΝΙΟΣΒΡΟΥΧΑΚΗΣ]

Congrats for 100.000 subs 🎉

[@learncommunolizer]

Thank you very much 🎉

[@tigerlg690]

Congrats 100,000 subscribers

[@learncommunolizer]

Thank you so much 😀🎉

[@aayanrout7791]

Congratulations sir for 100000 subs

[@learncommunolizer]

Thank you so much 😊 😊 😊 🙏🙏🙏

[@seekingCK]

from which grade is this?

[@zawatsky]

▫a²=±(a-1)²;
▫a²₁=(a₁-1)²=a²₁-2a₁+1;
▫1-2a₁=0;
▫2a₁=1;
▫a₁=½;
▫a²=-(a-1)²=-(a²-2a+1)=2a-a²-1;
▫2a²-2a+1=0;
▫D=4-4*2*1=4-8=-4;
▫√D=i√2;
▫a=(2±i√2)/4=2/4±i√2/4;
▫√2/4=√(2/16)=1/√8=1/(2√2);
▫a=½±i/(2√2);
▫a₂=½+i/(2√2);
▫a₃=½-i/(2√2).

[@tomtke7351]

I'm curious as to why only 3 solutions whereas we started with a^4

[@robertknapp7612]

Because the original equation has identical a^4 terms on both sides of the equation. Hence the problem is really only a cubic equation, hence the three solutions.

[@MathMasteryMinds]

Congratulations on your 100k subs 🎉

[@learncommunolizer]

Thank you very much 🎉🙏

[@MathMasteryMinds]

@@learncommunolizer I messaged you on WhatsApp

[@sanjaypriyadarshi]

❤❤❤❤❤

[@learncommunolizer]

❤️❤️❤️❤️❤️❤️

[@jean-pierrefuchs6553]

a=0 is also a solution

[@zygardezygote6204]

The substitution of zero into 'a' results in an incorrect equation.
0⁴ = (0 - 1)⁴
0 = (-1)⁴
0 = 1

[@User19rhx13xr]

1/2

[@vas880]

trivial solution

[@ajitanayak241]

Hi

[@learncommunolizer]

Hello 👋

[@АлександрМалык-ф5л]

А = 0,5. Ich nicht see video

[@tinhle-oj3gj]

Hi

[@learncommunolizer]

Hi, you are welcome
How are you