已知3(a²+b²+c²)=(a+b+c)²,求证:a=b=c
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/21 02:00:29
![已知3(a²+b²+c²)=(a+b+c)²,求证:a=b=c](/uploads/image/z/5303333-29-3.jpg?t=%E5%B7%B2%E7%9F%A53%EF%BC%88a%26%23178%3B%EF%BC%8Bb%26%23178%3B%EF%BC%8Bc%26%23178%3B%EF%BC%89%EF%BC%9D%EF%BC%88a%EF%BC%8Bb%EF%BC%8Bc%EF%BC%89%26%23178%3B%2C%E6%B1%82%E8%AF%81%EF%BC%9Aa%EF%BC%9Db%EF%BC%9Dc)
x){}KHTS64~; J:RE R:66X~,\d"}_`gC;o"XTQikmؤUH&%k'EjPst4pv
UcKm-0@! N!
已知3(a²+b²+c²)=(a+b+c)²,求证:a=b=c
已知3(a²+b²+c²)=(a+b+c)²,求证:a=b=c
已知3(a²+b²+c²)=(a+b+c)²,求证:a=b=c
3(a²+b²+c²)=(a+b+c)²
2a²+2b²+2c²=2ab+2ac+2bc
(a²-2ab+b²)+(b²-2bc+c²)+(a²-2ac+c²)=0
(a-b)²+(a-c)²+(b-c)²=0
∴a=b=c