若a,b,c属于正实数,且a+b+c=1,求证1/a^2+1/b^2+1/c^2≥27

a+b+c=1>=3(abc)^(1/3)
=>(abc)^(1/3)<=1/3
=>(abc)^(2/3)<=1/9
1/a^2+1/b^2+1/c^2>=3/(abc)^(2/3)>=3/(1/9)=27
取等a=b=c