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](/uploads/image/z/657731-11-1.jpg?t=%E5%B7%B2%E7%9F%A5a%2Cb%2Cc%E6%98%AF%E4%B8%89%E4%B8%AA%E6%9C%89%E7%90%86%E6%95%B0%2C%E4%B8%94a%26%23178%3B%2Bb%26%23178%3B%2Bc%26%23178%3B%3Dab%2Bac%2Bbc%E8%AF%95%E8%AF%B4%E6%98%8E%EF%BC%9Aa%3Db%3Dc)
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