BÀI KIỂM TRA BẤT ĐẲNG THỨC CHUẨN BỊ CHO VMO 2019

Problem. If a, b, c are nonnegative real numbers such that 2a 3 + 3b 2 + c ≤ 7 16 then a + b − c ≤ 3 4 . Proposed by Sladjan Stankovic 2. Problem. Let x,y, z be positive real numbers such that xyz (x + y + z) = 1. Prove that (x + y) (y + z) (z + x) ≥ 1 √ xz 3 » 4(x 6z 6 + 1) + 2(x + z) (x + y) (y + z) Proposed by Le Minh CuongProblem. If a, b, c are nonnegative real numbers such that 2a 3 + 3b 2 + c ≤ 7 16 then a + b − c ≤ 3 4 . Proposed by Sladjan Stankovic 2. Problem. Let x,y, z be positive real numbers such that xyz (x + y + z) = 1. Prove that (x + y) (y + z) (z + x) ≥ 1 √ xz 3 » 4(x 6z 6 + 1) + 2(x + z) (x + y) (y + z) Proposed by Le Minh CuongProblem. If a, b, c are nonnegative real numbers such that 2a 3 + 3b 2 + c ≤ 7 16 then a + b − c ≤ 3 4 . Proposed by Sladjan Stankovic 2. Problem. Let x,y, z be positive real numbers such that xyz (x + y + z) = 1. Prove that (x + y) (y + z) (z + x) ≥ 1 √ xz 3 » 4(x 6z 6 + 1) + 2(x + z) (x + y) (y + z) Proposed by Le Minh Cuong