利用基本不等式:1/x+1/y>=4/(x+y)故有:1/4x+1/4y>=1/(x+y)1/2a+1/2b+1/2c=1/4a+1/4b+1/4b+1/4c+1/4c+1/4a>=1/(a+b)+1/(b+c)+1/(c+a)
用1/2a+1/2b+1/2c减1/(b+c)+1/(a+c)+1/(a+b)即可!若正数,则1/2a+1/2b+1/2c>1/(b+c)+1/(a+c)+1/(a+b);若负数,则1/2a+1/2b+1/2c<1/(b+c)+1/(a+c)+1/(a+b)。