Home » Uncategorized » Inequality 31(Generalization, Vo Quoc Ba Can)

# Inequality 31(Generalization, Vo Quoc Ba Can)

Problem:

Let $\displaystyle a,b,c,d$ be positive real numbers. Prove that for $\displaystyle k\in \left[\frac{1}{2},2\right]$, the following inequality holds:

$\displaystyle \left(\frac{a+kb}{a+b+c}\right)^2+\left(\frac{b+kc}{b+c+d}\right)^2+\left(\frac{c+kd}{c+d+a}\right)^2+\left(\frac{d+ka}{d+a+b}\right)^2\geq \frac{4}{9}(k+1)^2$.

Solution:

Wrong soluion :(. Can, i wait for your solution on that problem 😀