Question

[titanic]

Chứng minh \(x^4+y^4\ge\frac{\left(x+y\right)^4}{8}\)

Answer 1

[Đinh Đức Hùng]

\(x^4+y^4\ge\frac{\left(x^2+y^2\right)^2}{2}\ge\frac{\left[\frac{\left(x+y\right)^2}{2}\right]^2}{2}=\frac{\left(x+y\right)^4}{8}\)(bđt Cauchy - Schwarz)