4

Part of 1998 Chile National Olympiad

Problems(1)

x^{3/2} + 6x^{5/4} + 8x^{3/4}\ge 15x (Chile NMO 1998 P4)

Source:

a) Prove that for any nonnegative real

x

x^{\frac32} + 6x^{\frac54} + 8x^{\frac34}\ge 15x.

b) Determine all x for which the equality holds

algebrainequalities