5

Part of 2020 Azerbaijan IZHO TST

Problems(1)

Source: Azerbaijan Math Olympiad Training

x,y,z

be positive real numbers such that

x^4+y^4+z^4=1

. Determine with proof the minimum value of

\frac{x^3}{1-x^8}+\frac{y^3}{1-y^8}+\frac{z^3}{1-z^8}