MathDB

2xy>1 or yz>1 than find the minimum value

Source: 2023 Turkey Egmo Tst P3

March 23, 2023

inequalitiesminimum value

Problem Statement

Let

x,y,z

be positive real numbers that satisfy at least one of the inequalities,

2xy>1

yz>1

. Find the least possible value of

xy^3z^2+\frac{4z}{x}-8yz-\frac{4}{yz}