- 求助一个不等式证明设a,b,c为任意实数.求证2∑a^6
- 设a,b,c为任意实数.求证
2∑a^6-6∑a^5*(b+c)+15∑a^4*(b^2+c^2)-4∑(bc)^3
-16abc∑a^3+16abc∑a^2*(b+c)-96(abc)^2≥0
- 设a,b,c为任意实数.求证
2∑a^6-6∑a^5*(b+c)+15∑a^4*(b^2+c^2)-4∑(bc)^3
-16abc∑a^3+16abc∑a^2*(b+c)-96(abc)^2≥0
分解如下
(b+c)^2*(4a-b-c)^2*(b-c)^2+(c+a)^2*(4b-c-a)^2*(c-a)^2
+(a+b)^2*(4c-a-b)^2*(a-b)^2>=0
取等条件为a:b:c=1:1:1,?醓:b:c=3:1:1