Only Geniuses Can Solve This | A Challenging Olympiad Problem

[@teilach]

2 also works

[@pedroteosousa]

5:54

[@wes9627]

I'm definitely not a genius, but my amoeba brain might try something like this. Substitute x=y+2 into the given equation and rearrange to: (y+2)^4-(y-2)^4=0 and note that even powers of y cancel out, leaving 2*4(2y^3+8y)=0, which has roots y=0 and y=±2i. Thus x=y+2=2 or 2±2i Check: x=2 is trivial. (2±2i-4)^4 = (-1)^4*(2±2i)^4 = (2±2i)^4 is easy to verify.

[@BlackSigma-iq4jy]

Or just take the 4th root on both sides. x-4=x, which gives -4=0 which is not true so this is not a solution, there's 2 solutions for this due to the plus or minus sign before the 4th root so, x-4=-x, then 2x=4, x=2

[@abhimaansnair5554]

why can't you just take the fourth root on both sides and then solve a simple linear equation.

[@Lokomotywcia]

Thought exactly the same

[@r3n_minecraft]

You get -4 = 0 which is obviously not true

[@Mortadelo_]

after the S : {2, 2+2i, 2-2i} the math stopped mathing for me