作业帮a>0,b>0,c>0,求证1/a+1/b+1/c>=2*[1/(a+b)+1/(b+c)+1/(c+a)]
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![a>0,b>0,c>0,求证1/a+1/b+1/c>=2*[1/(a+b)+1/(b+c)+1/(c+a)]](/uploads/image/z/11471050-10-0.jpg?t=a%3E0%2Cb%3E0%2Cc%3E0%2C%E6%B1%82%E8%AF%811%2Fa%2B1%2Fb%2B1%2Fc%3E%3D2%2A%5B1%2F%28a%2Bb%29%2B1%2F%28b%2Bc%29%2B1%2F%28c%2Ba%29%5D)
a>0,b>0,c>0,求证1/a+1/b+1/c>=2*[1/(a+b)+1/(b+c)+1/(c+a)]
a>0,b>0,c>0,求证1/a+1/b+1/c>=2*[1/(a+b)+1/(b+c)+1/(c+a)]
a>0,b>0,c>0,求证1/a+1/b+1/c>=2*[1/(a+b)+1/(b+c)+1/(c+a)]
1/a+1/b-4/(a+b) =[b(a+b)+a(a+b)-4ab)/[ab(a+b)] =(a-b)^2/[ab(a+b)] >=0当a=b等号成立 所以：1/a+1/b>=4/(a+b) 同理1/a+1/c>=4/(a+c),1/b+1/c>=4/(b+c) 相加：2(1/a+1/b+1/c)>=4[1/(a+b)+1/(b+c)+1/(a+c)] 所以：1/a+1/b+1/c>=2[1/(a+b)+1/(b+c)+1/(a+c)]