Question

da-ti-mi si mie va rog un exemplu la inegalitatea mediilor

Answer 1

$m_{h} \leq m_{g} \leq m_{a} \leq m_{p}$ adica :

Media armonica ≤ media geometrica ≤ media aritmetica ≤ media patratica

Pentru 2 numere:

$\frac{2}{ \frac{1}{a} + \frac{1}{b} } \leq \sqrt{ab} \leq \frac{a+b}{2} \leq \sqrt{ \frac{a^{2} + b^{2}}{2} }$

Pentru 3 numere:

$\frac{3}{ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} } \leq \sqrt[3]{abc} \leq \frac{a+b+c}{3} \leq \sqrt{ \frac{a^{2}+b^{2}+c^{2}}{3} }$