Let $a$ and $b$ be real numbers such that $a + b = 2$. Show that: $$\min \{|a|,|b|\} < 1 < \max \{|a|,|b|\} \Leftrightarrow a, b \in (-3,1)$$
Source: 1996 Romania NMO VIII p1
Tags: algebra, inequalities
Let $a$ and $b$ be real numbers such that $a + b = 2$. Show that: $$\min \{|a|,|b|\} < 1 < \max \{|a|,|b|\} \Leftrightarrow a, b \in (-3,1)$$