a,b,c为正实数,且a+b+c=1,求证1/a+1/b+1/c>=9
a,b,c为正实数,且a+b+c=1,求证1/a+1/b+1/c>=9
日期：2022-02-08 16:21:36 人气：1
已知a,b,c属于正实数,且a+b+c=1,求证1/a+1/b+1/c大于等于9
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+b/c+c/b+a/c+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+b/c+c/b+a/c+c