设a,b,c都是正数,求证:1/2a+1/2b+1/2c大于等于1/(b+c)+1/(a+c)+1/(a+b)

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设a,b,c都是正数,求证:1/2a+1/2b+1/2c大于等于1/(b+c)+1/(a+c)+1/(a+b)
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设a,b,c都是正数,求证:1/2a+1/2b+1/2c大于等于1/(b+c)+1/(a+c)+1/(a+b)
设a,b,c都是正数,求证:1/2a+1/2b+1/2c大于等于1/(b+c)+1/(a+c)+1/(a+b)

设a,b,c都是正数,求证:1/2a+1/2b+1/2c大于等于1/(b+c)+1/(a+c)+1/(a+b)
1/(b+c)+1/(a+c)+1/(a+b)<=1/(2(bc)^0.5)+1/(2(ac)^0.5)+1/(2(ab)^0.5)
1/2(bc)0.5<=1/4(1/b +1/c)
1/2(ac)0.5<=1/4(1/a +1/c)
1/2(ba)0.5<=1/4(1/b +1/a)
3式相加 得证