设a,b,c都是实数,且c>0.求证:a+cb/1+c介于a,b之间

Question

设a,b,c都是实数,且c>0.求证:a+cb/1+c 介于a,b之间

Answer 1

[a-(a+bc)/(1+c)]*[b-(a+bc)/(1+c)]=[1/(1+c)²]*[a+ac-a-bc]*[b+bc-a-bc]=-c*[1/(1+c)²]*(a-b)²因为c＞0,1/(1+c)²＞0,(a-b)²≥0,故-c*[1/(1+c)²]*(a-b)²≤0[a-(a+bc)/(1+c)]*[b-...