Bài 7
a) Có: \(\left(x-2\right)^2\ge0\) với mọi x
\(\Rightarrow\left(x-2\right)^2+5\ge5\)
\(\Rightarrow\dfrac{3}{\left(x-2\right)^2+5}\le\dfrac{3}{5}\)
\(\Rightarrow C_{max}=\dfrac{3}{5}\)
Dấu ''='' xảy ra khi \(\left(x-2\right)^2=0\Rightarrow x=2\)
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b) Có: \(\left(x-3\right)^2\ge0\) với mọi x
\(\left|y-5\right|\ge0\) với mọi y
\(\Rightarrow-10-\left(x-3\right)^2-\left|y-5\right|\le-10\)
\(\Rightarrow D_{max}=-10\)
Dấu ''='' xảy ra khi
\(\left\{{}\begin{matrix}\left(x-3\right)^2=0\\\left|y-5\right|=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=3\\y=5\end{matrix}\right.\)
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Bài 6
a) Có: \(\left(x-2\right)^2\ge0\) với mọi x
\(\Rightarrow\left(x-2\right)^2-1\ge-1\)
\(\Rightarrow A_{min}=-1\)
Dấu ''='' xảy ra khi \(\left(x-2\right)^2=0\Rightarrow x=2\)
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b) Có: \(\left(x^2-9\right)^2\ge0\) với mọi x
\(\left|y-2\right|\ge0\) với mọi y
\(\Rightarrow\left(x^2-9\right)^2+\left|y-2\right|+10\ge10\)
\(\Rightarrow B_{min}=10\)
Dấu ''='' xảy ra khi
\(\Rightarrow\left\{{}\begin{matrix}\left(x^2-9\right)^2=0\\\left|y-2\right|=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x^2=9\\y=2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\pm3\\y=2\end{matrix}\right.\)
Vậy...
