Problem

Source: Iran 3rd round 2011-algebra exam-p2

Tags: inequalities, inequalities proposed



For nonnegative real numbers $x,y,z$ and $t$ we know that $|x-y|+|y-z|+|z-t|+|t-x|=4$. Find the minimum of $x^2+y^2+z^2+t^2$. proposed by Mohammadmahdi Yazdi, Mohammad Ahmadi