已知a,b,c是三个有理数,且a²+b²+c²=ab+ac+bc试说明:a=b=c
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已知a,b,c是三个有理数,且a²+b²+c²=ab+ac+bc试说明:a=b=c
已知a,b,c是三个有理数,且a²+b²+c²=ab+ac+bc试说明:a=b=c
已知a,b,c是三个有理数,且a²+b²+c²=ab+ac+bc试说明:a=b=c
a²+b²+c²=ab+ac+bc
2a²+2b²+2c²=2ab+2ac+2bc
2a²+2b²+2c²-2ab-2ac-2bc=0
(a²-2ab+b²)+(a²-2ac+c²)+(b²-2bc+c²)=0
(a-b)²+(a-c)²+(b-c)²=0
∴{a-b=0
a-c=0
b-c=0
∴a=b=c