Question

Folosind inegalitatea mediilor dem:
x^3+y^3 >=x^2*y+x*y^2​

Answer 1

$\it x^3+y^3=(x+y)(x^2-xy+y^2)=(x+y)(x^2+y^2-xy)\geq(x+y)(2xy-xy)\Rightarrow\\ \\ \Rightarrow x^3+y^3\geq(x+y)\cdot xy \Rightarrow x^3+y^3\geq x^2y+xy^2$