Question

Cine ma poate ajuta cu exercitiul acesta?
(numarul 35)

Answer 1

[tex]1.\ 2a^2+2b^2+2c^2\geq 2ab+2bc+2ca\\ (a^2-2ab+b^2)+(b^2-2bc+c^2)+(a^2-2ac+c^2)\geq 0\\ (a-b)^2+(b-c)^2+(a-c)^2\geq 0 (A)\\ \\ 2. Aplicam~inegalitatea ~de~mai~sus~pentru:\\ a\rightarrow a^2\\ b\rightarrow b^2\\ c\rightarrow c^2\\ 3.a^4+b^4+c^4\geq a^2b^2+b^2c^2+a^2c^2\geq abbc+acbc+abac\\ =abc(a+b+c)[/tex]