[20分][高一不等式]已知a,b,c∈R+,且a+b+c=1,求证1/a+1/b+1/c≥9已知a,b,c∈R+,且a+b+c=1,求证1/a+1/b+1/c≥9请回答出解题过程,特别是重要的步骤,

Question

[20分][高一不等式]已知a,b,c∈R+,且a+b+c=1,求证1/a + 1/b + 1/c≥9
已知a,b,c∈R+,且a+b+c=1,求证1/a + 1/b + 1/c≥9
请回答出解题过程,特别是重要的步骤,

Answer 1

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/a+a/b+b/a
>=3+2+2+2
=9