已知△ABC的边a,b,c,满足a²+b²+c²+338=10a+24b+26c判断△ABC的形状
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/28 16:07:12
![已知△ABC的边a,b,c,满足a²+b²+c²+338=10a+24b+26c判断△ABC的形状](/uploads/image/z/4076171-35-1.jpg?t=%E5%B7%B2%E7%9F%A5%E2%96%B3ABC%E7%9A%84%E8%BE%B9a%2Cb%2Cc%2C%E6%BB%A1%E8%B6%B3a%26%23178%3B%2Bb%26%23178%3B%2Bc%26%23178%3B%2B338%3D10a%2B24b%2B26c%E5%88%A4%E6%96%AD%E2%96%B3ABC%E7%9A%84%E5%BD%A2%E7%8A%B6)
已知△ABC的边a,b,c,满足a²+b²+c²+338=10a+24b+26c判断△ABC的形状
已知△ABC的边a,b,c,满足a²+b²+c²+338=10a+24b+26c判断△ABC的形状
已知△ABC的边a,b,c,满足a²+b²+c²+338=10a+24b+26c判断△ABC的形状
移项
(a²-10a+25)+(b²-24b+144)+(c²-26c+169)=0
(a-5)²+(b-12)²+(c-13)²=0
所以a-5=b-12=c-13=0
a=5,b=12,c=13
则a²+b²=c²
所以是直角三角形