Edogawa Conan CTV Báo cáo sai phạm
Ta có: a2 + b2 + c2 + 3 = 2(a + b + c)
=> a2 + b2 + c2 + 3 - 2(a + b + c) = 0
=> a2 + b2 + c2 + 3 - 2a - 2b - 2c = 0
=> (a2 - 2a + 1) + (b2 - 2b + 1) + (c2 - 2c + 1) = 0
=> (a - 1)2 + (b - 1)2 + (c - 1)2 = 0
<=> \(\hept{\begin{cases}a-1=0\\b-1=0\\c-1=0\end{cases}}\) <=> a = b = c = 1
=> đpcm
Việt Hoàng CTV Báo cáo sai phạm
\(a^2+b^2+c^2+3=2\left(a+b+c\right)\)
\(\Leftrightarrow a^2+b^2+c^2+3-2\left(a+b+c\right)=0\)
\(\Leftrightarrow a^2+b^2+c^2+1+1+1-2a-2b-2c=0\)
\(\Leftrightarrow\left(a^2-2a+1\right)+\left(b^2-2b+1\right)+\left(c^2-2c+1\right)=0\)
\(\Leftrightarrow\left(a-1\right)^2+\left(b-1\right)^2+\left(c-1\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}a-1=0\\b-1=0\\c-1=0\end{cases}\Leftrightarrow\hept{\begin{cases}a=1\\b=1\\c=1\end{cases}\Leftrightarrow}a=b=c=1}\)
