Question

a) \(\left[m;m+2\right]\cap\left[-1;2\right]=\varnothing\) khi nào?

b) \(\left(\text{-∞; 9a }\right)\cap\left(\frac{4}{a};\text{+∞ }\right)\ne\varnothing\) khi nào?

c) \(\left(\text{-∞;a }\right)\cup\left(\frac{4}{a};\text{+∞ }\right)=R\) khi nào?

d) [ m-3; 9) có 7 phần tử nguyên khi nào?

Answer 1

a/ \(\left[m;m+2\right]\cap\left[-1;2\right]=\varnothing\)

\(\Leftrightarrow\left[{}\begin{matrix}m+2< -1\\m>2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}m< -3\\m>2\end{matrix}\right.\)

b/ \(\left(-\infty;9a\right)\cap\left(\frac{4}{a};+\infty\right)\ne\varnothing\)

\(\Leftrightarrow\left\{{}\begin{matrix}a\ne0\\\frac{4}{a}< 9a\end{matrix}\right.\) \(\Leftrightarrow\frac{\left(2a-3\right)\left(2a+3\right)}{a}>0\Rightarrow\left[{}\begin{matrix}a>\frac{3}{2}\\-\frac{3}{2}< a< 0\end{matrix}\right.\)

c/ \(\left(-\infty;a\right)\cup\left(\frac{4}{a};+\infty\right)=R\)

\(\Rightarrow\left\{{}\begin{matrix}a\ne0\\a>\frac{4}{a}\end{matrix}\right.\) \(\Rightarrow\frac{\left(a-2\right)\left(a+2\right)}{a}>0\Rightarrow\left[{}\begin{matrix}a>2\\-2< a< 0\end{matrix}\right.\)

d/ \([m-3;9)\) có 7 phần tử nguyên khi:

\(7\le9-\left(m-3\right)< 8\Rightarrow4< m\le5\)