已知a,b,c∈R,且a+b+c=1,求证1/a+1/b+1/c≥9
问题描述：
已知a,b,c∈R,且a+b+c=1,求证1/a+1/b+1/c≥9
答
∵a+b+c=1,a,b,c∈R+（否则不对）∴1/a+1/b+1/c=(a+b+c)/a+(a+b+c)/b+(a+b+c)/c=3+(b/a+a/b)+(b/c+c/b)+(c/a+a/c)∵a/b+b/a≥2√(a/b*b/a)=2（当a/b=b/a,a=b时,取等号）同理：b/c+c/b≥2,a/c+c/a≥2∴(b/a+a/b)+(b/c...