已知:a，b，c，均为正整数，且a b c=1 求证1/a 1/b 1/c大于等于9
已知:a，b，c，均为正整数，且a b c=1 求证1/a 1/b 1/c大于等于9
日期：2021-07-07 05:05:25 人气：1
已知:a，b，c，均为正整数，且a+b+c=1
求证1/a
1/b
1/c大于等于91/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/a+a/b+b/a
>=3
求证1/a
1/b
1/c大于等于91/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/a+a/b+b/a
>=3