Question

Cho `A={x in R` | `|x-m|=25} ; B={x in R` | `|x| >= 2020}` . Có bao nhiêu giá trị nguyên m thì \(A\cap B=\varnothing\)

Answer 1

\(\left|x-m\right|=25\Leftrightarrow\left[{}\begin{matrix}x=m+25\\x=m-25\end{matrix}\right.\)

\(\left|x\right|\ge2020\Leftrightarrow\left[{}\begin{matrix}x\ge2020\\x\le-2020\end{matrix}\right.\)

+) \(x=m+25\)

Để \(A\cap B=\varnothing\) \(\Leftrightarrow\left\{{}\begin{matrix}m+25>-2020\\m+25< 2020\end{matrix}\right.\)\(\Leftrightarrow-2045< m< 1995\)

+) \(x=m-25\)

Để \(A\cap B=\varnothing\)  \(\Leftrightarrow\left\{{}\begin{matrix}m-25>-2020\\m-25< 2020\end{matrix}\right.\)\(\Leftrightarrow-1995< m< 2045\)