Question

已知正数a,b,c,满足a+b+c=1,求证（1/a)+(1/b)+(1/c)>=9和(1/a -1)(1/b -1)(

Answer 1

1=(a+b+c)^3>=27abc abc<=1/27

(1/a+1/b+1/c)^3>=27/abc>=27*27

1/a+1/b+1/c>=9

(1/a-1)(1/b-1)(1/c-1)=(a+b)(b+c)(c+a)/(abc)

(a+b)^2>=4ab

(a+b)^2*(b+c)^2*(c+a)^2>=64aabbcc

(1/a-1)(1/b-1)(1/c-1)=(a+b)(b+c)(c+a)/(abc)>=8