a^3+b^3+c^3+(1/a+1/b+1/c)^3大于等于18_数学解答

a^3+b^3+c^3+(1/a+1/b+1/c)^3大于等于18

人气：172 ℃　时间：2020-05-01 02:14:22

解答

a^3+b^3+c^3+(1/a+1/b+1/c)^3
≥3(a^3.b^3.c^3)^(1/3)+[3(1/a.1/b.1/c)^(1/3)]^3
=3abc+(27/abc)
≥2√(3abc*27/abc)
=2√81
=18