Question

已知a大于0,b大于0,c大于0,d大于0,求证(a+b+c+d)/2大于等于根号ab+根号cd

Answer 1

(a+b+c+d)/2大于等于根号ab+根号cd

(a+b+c+d)/2=(a+b)/2+(c+d)/2

(a+b)/2大于等于根号ab

(c+d)/2大于等于根号 cd

所以(a+b+c+d)/2大于等于根号ab+根号cd