Question

一道高二不等式证明a b c 为正数 求证(a+b+c)(1/a+1/b+1/c)≥9

Answer 1

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

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

=3+(a/b+b/a)+(a/c+c/a)+(b/c+c/b)

>=3+2+2+2=9

当且仅当a=b=c时等号成立