a、b、c都是正实数,求证：(b+c)/2a+(a+c)/2b+(a+b)/2c>=2a/(b+c)+2b/(a+c)+2c/(a_数学解答

a、b、c都是正实数,求证：(b+c)/2a+(a+c)/2b+(a+b)/2c>=2a/(b+c)+2b/(a+c)+2c/(a+b),

人气：364 ℃　时间：2020-02-05 19:50:29

解答

(b+c)/2a+(a+c)/2b+(a+b)/2c>=2a/(b+c)+2b/(a+c)+2c/(a+b),=b/2a+c/2a+a/2b+c/2b+a/2c+b/2c-2a/(b+c)-2b/(a+c)-2c/(a+b)=b/2a+b/2c-2b/(a+c) + c/2a+c/2b-2c/(a+b) + a/2c+a/2b-2a/(b+c)b/2a+b/2c-2b/(a+c)=b(1/2a+1...