a: \(x^2+4xy\ge-4y^2\)
=>\(x^2+4xy+4y^2\ge0\)
=>\(x^2+2\cdot x\cdot2y+\left(2y\right)^2\ge0\)
=>\(\left(x+2y\right)^2\ge0\) (luôn đúng)
b: \(\left(x+y\right)^2\ge4xy\)
=>\(x^2+2xy+y^2\ge4xy\)
=>\(x^2+2xy+y^2-4xy\ge0\)
=>\(x^2-2xy+y^2\ge0\)
=>\(\left(x-y\right)^2\ge0\) (luôn đúng)
c: \(x^3+y^3\ge x^2y+xy^2\)
=>\(x^3+y^3-x^2y-xy^2\ge0\)
=>\(x^2\left(x-y\right)-y^2\left(x-y\right)\ge0\)
=>\(\left(x-y\right)\left(x^2-y^2\right)\ge0\)
=>\(\left(x-y\right)\left(x-y\right)\left(x+y\right)\ge0\)
=>\(\left(x-y\right)^2\left(x+y\right)\ge0\)
mà \(\left(x-y\right)^2\ge0\forall x,y>0;\left(x+y\right)^2>0\forall x,y>0\)
nên \(\left(x-y\right)^2\left(x+y\right)\ge0\forall x,y>0\)
=>ĐPCM
