- 不等式问题㈢见附图
- 不等式问题㈢见附图
- 作置换:x→a^2,y→b^2,z→c^2.
{∑a√[a^4+b^4+c^4+bc)^2]}^2
=∑a^6+∑(b^2+c^2)a^4+3(abc)^2+2∑bc√[∑a^4+(ca)^2,∑a^4+(ab)^2]
≥∑a^6+∑(b^2+c^2)a^4+3(abc)^2+2∑(b+c)a^5+2abc∑a^3+6(abc)^2
=∑a^6+∑(b^2+c^2)a^4+9(abc)^2+2∑(b+c)a^5+2abc∑a^3
＝＝＞
∑a^6+∑(b^2+c^2)a^4+9(abc)^2+2∑(b+c)a^5+2abc∑a^3≥4∑a^2*∑(bc)^2
＜＝＝＝＞
∑a^6-3∑(b^2+c^2)a^4-3(abc)^2+2∑(b+c)a^5+2abc∑a^3≥0
设a=min(a,b,c),上式分解得:
a[a^3+3(b+c)a^2+7abc+4bc(b+c)]*(a-b)*(a-c)+
[b^4+c^4+4bc(b^2+c^2)+4(bc)^2+2a(b+c)^3-(3b^2+3c^2+2bc)a^2]*(b-c)^2≥0
上式为显然。