Here is another challenging problem from the 2004 Pi in the Sky Canadian magazine for high school students.
“Problem 4. Find the real solutions of the system
________________ (x + y)^5 = z,
________________ (y + z)^5 = x,
________________ (z + x)^5 = y.”
See the Quintic Nightmare
The answer published by you is X = 0 or ±1/(2*√2)
In my opinion ±1/(2*√2) should be ±1 divided by fourth root of 32 i.e. ±1/(32^0.25).
I hope I am not missing anything.
You are correct. My bad. Instead of the square root of 2 it should have been the fourth root of 2. Thanks for catching that.