Question

[huỳnh thị ngọc ngân]

biết

\(a^2+b^2+c^2+14=2a+4b+6c\)

vậy a+b+c=?

Answer 1

[Trần Hữu Tuyển]

\(a^2+b^2+c^2+14-2a-4b-6c=0\)

\(\Leftrightarrow\left(a-1\right)^2+\left(b-2\right)^2+\left(c-3\right)^2=0\)

mà \(\left(a-1\right)^2\ge0;\left(b-2\right)^2\ge0;\left(c-3\right)^2\ge0\)nên

\(\left\{{}\begin{matrix}a-1=0\\b-2=0\\c-3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=1\\b=2\\c=3\end{matrix}\right.\)