设a,b,c均为实数,求证:1/2a+1/2b+1/2c>=1/(b+c)+1/(a+c)+1/(a+b)

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设a,b,c均为实数,求证:1/2a+1/2b+1/2c>=1/(b+c)+1/(a+c)+1/(a+b)
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设a,b,c均为实数,求证:1/2a+1/2b+1/2c>=1/(b+c)+1/(a+c)+1/(a+b)
设a,b,c均为实数,求证:1/2a+1/2b+1/2c>=1/(b+c)+1/(a+c)+1/(a+b)

设a,b,c均为实数,求证:1/2a+1/2b+1/2c>=1/(b+c)+1/(a+c)+1/(a+b)
a,b,c均是正实数才可求证.
反例a=-1,b=-2,c=3
左式为负,右式为正,命题为假命题.
若a,b,c均是正数,易证1/a+1/b>=4/(a+b)
同理有1/a+1/c>=4/(a+c)
1/b+1/c>=4/(a+c)
三式相加则得到命中的式子.