Question

Cho: a² + b² + c² + 3 = 2(a + b + c)

Chứng minh a = b = c = 1

Answer 1

Bạn ghi sai đề rồi: Cm:a=b=c=1.

Ta có : \(a^2+b^2+c^2+3=2\left(a+b+c\right)\)

\(\Leftrightarrow a^2+b^2+c^2+3-2a-2b-2c=0\)

\(\Leftrightarrow a^2-2a+1+b^2-2b+1+c^2-2c+1=0\)

\(\Leftrightarrow\left(a-1\right)^2+\left(b-1\right)^2+\left(c-1\right)^2=0\)

\(\Leftrightarrow\hept{\begin{cases}\left(a-1\right)^2=0\\\left(b-1\right)^2=0\\\left(c-1\right)^2=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}a-1=0\\b-1=0\\c-1=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}a=1\\b=1\\c=1\end{cases}\Leftrightarrow a=b=c=1\left(ĐPCM\right)}\)