Question

已知△ABC的三边长分别为a,b,c,周长为6,且a^2+b^2+c^2=ab+bc+ca,则△ABC的三边长分别为?

Answer 1

a²+b²+c²=ab+bc+ca => 2(a²+b²+c²)=2(ab+bc+ca) => (a²+b²-2ab) +(b²+c²-2bc)+( a²+c²-2ca)=0

=> (a-b)²+(b-c)²+(c-a)²=0 => a=b=c

△ABC的三边长分别为a,b,c,周长为6,=>a+b+c=6 => a=b=c=2