Question

已知a,b,c是三角形abc的三边,满足a^+b^+c^-ab-bc-ca=0,试判断△abc的形状,

Answer 1

a^2+b^2+c^2-ab-bc-ca=0

等式两边同时乘以2

2a^2+2b^2+2c^2-2ab-2bc-2ca=0

(a^2-2ab+b^2)+(b^2-2bc+c^2)+(c^2-2ca+a^2)=0

(a-b)^2+(b-c)^2+(c-a)^2=0

a=b

b=c

c=a

a=b=c

等边三角形