设实数a,b,c都>=1,且满足：abc+2a^2+2b^2+2c^2+ca-cb-4a+4b-c=28,求a+b+c的最大值

解 由2(6-a-b-c)\left[5a+8b+8c-21+2(b-1)(c-1)+3(c-1)(a-1)+2(a-1)(b-1)\right]=(a+2b+2c-5)\left(28+4a-4b+c-2a^2-2b^2-2c^2+bc-ca-abc\right)+(a-3)^2\left[2a+b-3+(b-1)(c-1)\right]+2(b-1)^2\left[2b-2+(c-1)(a...