已知a丨c丨>丨a丨,化简丨a+c丨+丨b+c丨-丨a-b丨.

问题描述:

已知a丨c丨>丨a丨,化简丨a+c丨+丨b+c丨-丨a-b丨.

a0
b丨b丨>丨c丨>丨a丨
b丨a+c丨+丨b+c丨-丨a-b丨
=a+c-(b+c)-(a-b)
=0

∵a0,丨b丨>丨c丨>丨a丨
∴b∴丨a+c丨+丨b+c丨-丨a-b丨
=a+c+(-b-c)-(a-b)
=a+c-b-c-a+b
=0

由a丨a丨
得 a+c>0 b+c0
丨a+c丨+丨b+c丨-丨a-b丨
=a+c-b-c-a+b
=0