Question

证明不等式：a.b.c∈R,a^4+b^4+c^4≥abc(a+b+c)

Answer 1

a^4+b^4>=2a^2*b^2a^4+c^4>=2a^2*c^22a^4+b^4+c^4>=4a^2*bc同理2b^4+c^4+a^4>=4ab^2*c2c^4+a^4+b^4>=4abc^2相加4a^4+4b^4+4c^4>=4a^2*bc+4ab^2*c+4abc^2即a^4+b^4+c^4>=abc(a+b+c)当a=b=c时取得等号