【数学】已知△ABC的三边长a,b,c满足等式a²-c²+2ab-2bc=0,试说明△ABC是等腰三角形
人气：314 ℃ 时间：2020-03-27 10:24:07
解答
a²-c²+2ab-2bc=0
(a²-c²)+(2ab-2bc)=0
(a+c)(a-c)+2b(a-c)=0
(a-c)(a+c+2b)=0
∵a+c+2b>0
∴a-c=0
即a=c
∴△ABC是等腰三角形
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