若a,b,c>0,求证:1/2a+1/2b+1/2c>=1/(a+b)+1/(b+c)+1/(c+a)

若a,b,c>0,求证:1/2a+1/2b+1/2c>=1/(a+b)+1/(b+c)+1/(c+a)
若a,b,c>0,求证:1/2a+1/2b+1/2c>=1/(a+b)+1/(b+c)+1/(c+a)

若a,b,c>0,求证:1/2a+1/2b+1/2c>=1/(a+b)+1/(b+c)+1/(c+a)
(1/a+1/b)(a+b)=2+a/b+b/a>=4
所以(1/a+1/b)/4>=1/(a+b)
类似得到(1/b+1/c)/4>=1/(b+c)
(1/c+1/a)/4>=1/(c+a)
相加即可

把等号后面的那个式子改成分式你就能看出来了