若△ABC的三边长a,b,c满足a³-a²b+ab²-ac²+bc²-b³=0,试判断△ABC的形状

若△ABC的三边长a,b,c满足a³-a²b+ab²-ac²+bc²-b³=0,试判断△ABC的形状
若△ABC的三边长a,b,c满足a³-a²b+ab²-ac²+bc²-b³=0,试判断△ABC的形状

若△ABC的三边长a,b,c满足a³-a²b+ab²-ac²+bc²-b³=0,试判断△ABC的形状
a³-a²b+ab²-ac²+bc²-b³＝0
→(a³-b³)-(a²b-ab²)-(ac²-bc²)＝0
→(a-b)(a²+ab+b²)-ab(a-b)-c²(a-b)＝0
→(a-b)(a²+ab+b²-ab-c²)＝0
→(a-b)(a²+b²-c²)＝0
→a＝b或a²+b²＝c².
可见,△ABC是等腰三角形或直角三角形.