It is known that the lengths of three sides of △ ABC are a, B, C respectively, and satisfy a & # 178; + C & # 178; = 2Ab + 2bc-2b & # 178;. It is proved that △ ABC is an equilateral triangle

It is known that the lengths of three sides of △ ABC are a, B, C respectively, and satisfy a & # 178; + C & # 178; = 2Ab + 2bc-2b & # 178;. It is proved that △ ABC is an equilateral triangle

a²+c²=2ab+2bc-2b²
a²-2ab+b²+b²-2bc+c²=0
﹙a-b﹚²+﹙b-c﹚²=0
∵﹙a-b﹚²≥0,﹙b-c﹚²≥0
∴a-b=0,a=b
b-c=0,b=c
a=b=c

Elden Ring Premiere

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