Question

△ABC的三边ABC满足a+b+c=3/2乘以根号2,a²+b²+c²=3/2,试判断△A

Answer 1

∵a+b+c=3/2*√2

∴a^2+b^2+c^2+2(ab+bc+ac)=9/2

又∵a^2+b^2+c^2=3/2

∴2(ab+bc+ac)=2a^2+2b^2+2c^2

移项有

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

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

所以a=b=c

所以△ABC是等边三角形