Olympiad Mathematics, fully solved | Can you solve this?

This is beautifully solved for you guys #maths #equation #mathematics #algebra #mathstricks #olympiad #exponential #exponentialequation #education

[mastsu]

これ、最初に2x-4=yとおけばy^4=16になるからy=±2, ±2i=2x-4、なので全体を2で割ってx-2=±1, ±iになりx=2±1, 2±iだからx=1, 3, 2+i, 2-iとすぐわかる。

[Awesomekat.]

U went a long way..u just need to plug the 4th root both sides and within three steps u are done...

[wrainerinc.]

(2x-4)^4=2^4e^(i2πn)
2x-4=2e^(i2πn/4)
x=e^(i2πn/4)+2 n=0 1, 2, 3
=3, 2+i, 1, 2-i

[marisuki]

(2x-4)^4=16
(2x-4)^4=2^4 or -2^4
2x-4=2 or -2
x-2=1 or -1
x=3 or 1

[opytmx]

Yes, of course there are 4 solutions. But why so much calculation effort?
(2x - 4)^2 = +/-4 shows directly the 2 pairs for the solutions:
For I & II) 2x - 4 = 2 and 2x - 4 = -2, and for III & IV) 2x - 4 = 2i and 2x - 4 = -2i.
Divided by 2 and + 2 they result immediately in x = 3, x = 1, x = 2 + i and x = 2 - i. 🙂

[pat]

Of course, 4 solutions : 2x - 4 = 2 ; 2x - 4 = -2 ; 2x - 4 = 2i ; 2x - 4 = -2i

[pra]

1:08 well, why don't you just do the same thing on previous step?
√[(2x-4)²]=√(±4)
2x-4=±2 or ±2i
2x=4±2or 4±2i
x=2±1 or 2±i
x=1 or 3 or 2+i or 2-i

[ElOpa]

No se porqué la complicaron tanto. Pasas la raíz 4 al otro lado y queda 2 ó -2, pasás el 4 sumando y te queda 6 ó 2, pasas el 2 dividiendo y te queda 3 ó 1

[sob-jzfg]

Everybody can solve it in their mind without writing down all the equations one by one.

[FernandoBarretto]

(2x-4)^4 = 2^4 => (2x-4) = 2 => x=3

[Shuu-Ko]

ものすごく効率が悪い。初めから2x-4を2(x-2) で(x-2) をXか何かにすればもっと早く解ける

[isabelyflorencio]

This exercise has at least three ways to solve it. All are didactically interesting. I challenge you to find them

[pedrobarbosa]

Na verdade sao apresentadas 4 soluções porem so duas servem de verdade. 3 ou 1.

[bessardphilippe]

Chiotte les mathématiques modernes qui ne servent à rien dans la vie courante quand on voit des gens qui ne savent plus compter correctement et comprendre un texte de grammaire, l'histoire, la géographie

[davidettinger]

Bien long pour une équation d'assez simple.

[druunito]

Terrible solution.
2^4x(x-2)^4=2^4
(x-2)^4=1
(x-2)^4-1=0
((x-2)^2-1)((x-2)^2+1)=0
(x-2-1)(x-2+1)(x^2-4x+5)=0
x=3, x=1, 3rd bracket - no real solutions

[enriqueserranozuniga]

Desmasiadas vueltas para algo tan simple.