>>613
(a+1/a)(a+1/b)+(b+1/b)(b+1/c)+(c+1/c)(c+1/a)
= a^2+1+(a/b)+1/(ab)+b^2+1+(b/c)+1/(bc)+c^2+1+(c/a)+1/(ca)
= a^2+b^2+c^2+3+(a/b)+(b/c)+(c/a)+(a+b+c)/(abc)
= a^2+b^2+c^2+3+(a/b)+(b/c)+(c/a)+(a+b+c)^3/(abc)
≧ 1/3+3+3+3^3　（等号は a=b=c=1/3）
= 100/3