Question

已知a的平方加b的平方加c的平方等于ac加bc加ab,试证a等于b等于c

Answer 1

2*(a^2+b^2+c^2)=2ab+2ac+2bc

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

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

即a=b=c