7

Part of 2016 Tuymaada Olympiad

Problems(1)

Nonsymmetric Inequality

Source: Tuymaada 2016, P7, Seniors

x

y

z>{3\over 2}

prove the inequality x^{24} + \root 5\of {y^{60}+z^{40}} \geq \left(x^4 y^3 + {1\over 3} y^2 z^2 + {1\over 9} x^3 z^3 \right)^2.

inequalitiesinequalities proposed