求证:1⼀2a+1⼀2b+1⼀2c大于等于1⼀a+b +1⼀b+c +1⼀c+a

2025-01-04 00:03:11
推荐回答(1个)
回答1:

1/4a+1/4b
=(a+b)/4ab
≥(a+b)/(a+b)^2
=1/(a+b)
同理1/4b+1/4c≥1/(b+c)
1/4c+1/4a≥1/(c+a)
由以上三式可得1/2a+1/2b+1/2c≥1/(a+b)+1/(b+c)+1/(c+a)