Question

Chứng minh: 

Nếu a^2+b^2+c^2=ab+ac+bc thì a=b=c

Answer 1

Ta có : \(a^2+b^2+c^2=ab+bc+ac\Leftrightarrow2\left(a^2+b^2+c^2\right)=2\left(ab+bc+ac\right)\Leftrightarrow\left(a^2-2ab+b^2\right)+\left(b^2-2bc+c^2\right)+\left(c^2-2ac+a^2\right)=0\)

\(\Leftrightarrow\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2=0\) \(\Leftrightarrow\begin{cases}\left(a-b\right)^2=0\\\left(b-c\right)^2=0\\\left(c-a\right)^2=0\end{cases}\) \(\Leftrightarrow a=b=c\) 

Answer 2

2a²+2b²+2c²-2ab-2ac-2bc=0

(a²-2ab+b²)+(b²-2bc+c²)+(a²-2ac+c²)=0

(a²-b²)+(b²-c²)+(a²-c²)=0

=>(a²-b²)=0

     (b²-c²)=0

    (a²-c²)=0

→a=b=c 

Answer 3

trả lời nhanh giùm mình nhé