Question

x,y-nr reale pozitive
a)x³+y³≥x²y+xy²

Answer 1

$x^{3}+ y^{3}=(x+y)( x^{2} +xy+ y^{2})$
$x^{2} y+x y^{2}=xy(x+y)$
$(x+y)( x^{2} +xy+ y^{2}) \geq (x+y)( x^{2} + y^{2})$
($x^{2} +xy+ y^{2} \geq x^{2} + y^{2}$
$xy \geq 0$
ceea ce trebuia de demonstrat