Zbiory z wielomianem

[kamil1014]

Wyznacz \(\displaystyle{ A \cap B, B-A}\), gdy:
\(\displaystyle{ A={x \in R \wedge x ^{4}- 2x^{3}- 3x^{2} \ge 0}}\),
\(\displaystyle{ B={x \in R \wedge |3-4x| \le 5}}\).

[mmoonniiaa]

\(\displaystyle{ A: x^2(x^2-2x-3) \ge 0 \Leftrightarrow x^2(x+1)(x-3) \ge 0 \Leftrightarrow \\ \Leftrightarrow x \in (- \infty ;-1>\cup\{0\}\cup<3;+ \infty )\\
B: \begin{cases} 3-4x \le 5 \\ 3-4x \ge -5\end{cases} \Leftrightarrow \begin{cases} x \ge - \frac{1}{2} \\ x \le 2 \end{cases} \Leftrightarrow x \in <- \frac{1}{2} ;2>\\
A \cap B=\{0\}\\
B-A=<- \frac{1}{2} ;0)\cup(0;2>}\)