Question

[Ngọc ANh]

cho a^2+b^2+c^2=ab+bc+ca

chứng minh a=b=c

Answer 1

[Nguyễn Anh Quân]

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

<=>2a^2+2b^2+2c^2=2ab+2bc+2ca

<=>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=0 ; b-c=0 ; c-a=0

<=> a=b=c

=>ĐPCM

Answer 2

[Ngọc ANh]

thank you