Ta có:

\(\left[{}\begin{matrix}\left|x-2217\right|=\left|2217-x\right|\ge2217-x\\\left|x-200\right|\ge x-200\end{matrix}\right.\)

\(\Rightarrow\left|x-2217\right|+\left|x-200\right|\ge\left(2217-x\right)+\left(x-200\right)\)

\(\Rightarrow A\ge2217-x+x-200\)

\(\Rightarrow A\ge2017\)

Đẳng thức xảy ra \(\Leftrightarrow\left[{}\begin{matrix}\left|2217-x\right|=2217-x\\\left|x-200\right|=x-200\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2217-x\ge0\\x-200\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x\le2217\\x\ge200\end{matrix}\right.\)

\(\Leftrightarrow200\le x\le2217\)

\(\Rightarrow Min_A=2017\Leftrightarrow200\le x\le2217\)

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

\(\dfrac{x^2}{9}=\dfrac{y^2}{16}=\dfrac{x^2+y^2}{9+16}=\dfrac{100}{25}=4\)

\(\Rightarrow x^2=36\Rightarrow x=\pm6\)

\(\Rightarrow x^2=64\Rightarrow x=\pm8\)

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