Question

E2. Fie a,b numere reale pozitive. Sa se arate ca :

Answer 1

Răspuns:

$\frac{ a+b }{ 2 } < \sqrt{ \frac{ a ^ { 2 } +b ^ { 2 } }{ 2 } }$

$\left\{\begin{matrix}\\b\neq a\text{, }&\text{unconditionally}\\b\leq -a\text{, }&a\neq 0\\b\in (-\infty,0)\cup (0,-a]\text{, }&a\leq 0\end{matrix}\right.$

$\left\{\begin{matrix}\\a\neq b\text{, }&\text{unconditionally}\\a\leq -b\text{, }&b\neq 0\\a\in (-\infty,0)\cup (0,-b]\text{, }&b\leq 0\end{matrix}\right.$