$x^5 + y^5 - (x^4y + xy^4) $$= x^5 - x^4y + y^5 - xy^4 $$= x^4(x - y) + y^4(y - x) $$= (x^4 - y^4)(x - y) $$= (x + y)(x - y)^2(x^2 + y^2) \geqslant 0 $$đpcm$
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để ......................\Rightarrow x^5 + y^5 - (x^4y + xy^4)
\geqslant 0$$= x^5 - x^4y + y^5 - xy^4 $$= x^4(x - y) + y^4(y - x) $$= (x^4 - y^4)(x - y) $$= (x + y)(x - y)^2(x^2 + y^2) \geqslant 0 $$đpcm$