已知x,y为有理数,证明a²++b²+c²-ac-bc-ac≥0
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已知x,y为有理数,证明a²++b²+c²-ac-bc-ac≥0
已知x,y为有理数,证明a²++b²+c²-ac-bc-ac≥0
已知x,y为有理数,证明a²++b²+c²-ac-bc-ac≥0
a²+b²+c²-ab-bc-ac
=(2a²+2b²+2c²-2ab-2bc-2ac)/2
=[(a²-2ab+b²)+(b²-2bc+c²)+(c²-2ac+a²)]/2
=[(a-b)²+(b-c)²+(c-a)²]/2≥0
命题得证