A Nice Math Olympiad Question x^6={x-1}^6 | Solve For 'X'

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[@869dailymathematics]

Please subscribe and like the video❤❤

[@b.mtaseenifaz9808]

you can just root over the equations giving you +-(x-1) resulting in 2x=1 and hence x=1/2. Keep it simple and subtle.

[@decentsingersclub]

isnt it just x = abs(x-1) ??

[@umarus2]

🤣 you destroyed 13-min video 😂

[@FinBoyXD]

You also need absolute value around x on the left, although it doesn't give any solutions when x is negative, it's still supposed to be there.

[@edwardkey7061]

I think this is way over complicated. This just becomes x = x-1 or 1-x. If the first is true than 1=0 which is never true and so the second option must be true. 1-x =x so x=1/2. I don’t know how time pressured it is. Maybe I would check other alternatives if you had like 5-10 mins a question, but for this, just keep it simple.

[@decentsingersclub]

you mean x = abs(x-1)

[@drice1985]

there is wrong formula:
a^3+b^3 = (a+b)(a^2-ab+b^) at minute 4:18

[@869dailymathematics]

Really??
I don't think so 🤔

[@franklyncheatum2324]

@@869dailymathematics You have a^3+b^3=(a+b)(a^2+ab+b^2) and that isn't right. If all the terms are positive, nothing cancels out in the middle and you end up with positive a^2b and ab^2. Also, let a=2 and b=1. 8+1 is not equal to (3)(4+2+1)=21.
@drice1985 is correct except he's missing the last 2 before the closing parentheses. 8+1=(3)(4-2+1)=(3)(3)=9

[@almighty_rex]

0.5

[@869dailymathematics]

Correct

[@eclips4385]

I just used the 6th root of unity and find 1/2 much faster and i got the complex solutions in addition

[@utsavmaitra9839]

wait cant you just say that (x-1)/x = exp(ni . pi/3)? since x=0 does not work

[@mak4rno]

nice nails bro

[@869dailymathematics]

😂😂😂😂

[@ImBatuAhhh]

1/2 or 0.5 too easy

[@869dailymathematics]

Correct

[@itodoregina5698]

Wiw nice one. Good❤🎉

[@869dailymathematics]

Thanks 🤗