已知实数a,b,c满足a2+b2+c2=1,则ab+bc+ca的取值范围是

问题描述:

已知实数a,b,c满足a2+b2+c2=1,则ab+bc+ca的取值范围是

2a2+2v2+2c2=2
a2+b2大于等于2ab同理2ab+2bc+2ca小于2
a2+b2大于等于-ab同理2ab+2ac+2bc大于-2

2a2+2v2+2c2=2
abc同号时,a2+b2>=2ab,c2+b2>=2cb,a2+c2>=2ac,不等号2边同加 得:2=2a2+2v2+2c2>= 2ab+2bc+2ca
a=b=c=(根号3)/3时,ab+bc+ca=1,所以ab+bc+ca