证明:a4+b4+c4>=abc(a+b+c)

a^4+b^4+c^4=1/2(a^4+b^4+a^4+c^4+b^4+c^4)
≥1/2(2a^2*b^2+2a^2*c^2+2b^2*c^2)=a^2*b^2+a^2*c^2+b^2*c^2
=1/2(a^2*b^2+a^2*c^2+a^2*b^2+b^2*c^2+a^2*c^2+b^2*c^2)
=1/2(a^2*(b^2+c^2)+b^2*(a^2+c^2)+c^2*(a^2+b^2))
≥1/2(a^2*2bc+b^2*2ac+c^2*2ab)
=a^2bc+b^2*ac+c^2*ab
=abc(a+b+c)
对于任何实数都成立.