已知a>0,b>0,c>0且a+b+c=1,求证a/1+b/1+c/1≥9

已知a>0,b>0,c>0,a+b+c=1,求证1/a+1/b+1/c≥9 (a+b+c)(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+(a/b+b/a)+(a/c+c/a)+(b/c+c/b) ≥3+2+2+2=9