Tìm a, b, c (đề thi học sinh giỏi toán 9)

T

tathivanchung

Ta có:
$ 4a^2 + 2b^2 + 2c^2 + 4ab - 2bc + 2b - 10c + 17=(2a+b)^2+(b-c+1)^2+(c-4)^2$ \geq $0$ \forall $a,b,c$
\Leftrightarrow $\left\{\begin{matrix}2a+b=0 & \\ b-c+1=0 & \\ c-4=0 &\end{matrix}\right.$
\Leftrightarrow $\left\{\begin{matrix}a=\frac{-3}{2} & \\ b=3 & \\ c=4 &\end{matrix}\right.$
 
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