a+b=c=1证明根号A＋根号B＋根号C＜＝根号3

证明：利用算术平均

题目错了吧 a+b+c=1
柯西不等式(∑ai^2) * (∑bi^2) ≥ (∑ai *bi)^2.
（1+1+1）*（a+b+c）≥（根号A＋根号B＋根号C）²
=》根号A＋根号B＋根号C＜＝根号3

因为:(根号a＋根号b＋根号c)^2
=a+b+c+2根号ab+2根号ac+2根号bc
=1+2根号ab+2根号ac+2根号bc
＜＝1+(a+b)+(a+c)+(b+c)
=3
所以:根号a＋根号b＋根号c＜＝根号3