mg[tex] \leq [/tex]ma
Pentru a demonstra inegalitatea putem lua ma si mg a doua nr. a si b.
[tex]mg= \sqrt{ab} [/tex]
[tex]ma= \frac{a+b}{2} [/tex]
Si inlocuim:
[tex]\sqrt{ab} \leq \frac{a+b}{2}[/tex] |*2
[tex]2 \sqrt{ab}\leq a+b[/tex] | ridicam la patrat
[tex]4ab \leq a^{2}+ 2ab+b^{2}[/tex]
[tex] a^{2}+ b^{2}+2ab-4ab \geq 0 [/tex]
[tex]a^{2}-2ab + b^{2} \geq 0[/tex]
[tex](a-b) ^{2} \geq 0[/tex], adevarat
rezulta ceea ce trebuia demonstrat
