Đáp án:
\(\begin{array}{l}
a)\left[ \begin{array}{l}
x \ge \sqrt 2 \\
x \le - \sqrt 2
\end{array} \right.\\
c)x \in \emptyset \\
d)\dfrac{1}{2} \ge x \ge - \dfrac{1}{2}
\end{array}\)
e) \(1 \ge x \ge - \dfrac{5}{2}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)DK:{x^2} - 3 \ge 0\\
\to {x^2} \ge 3\\
\to \left[ \begin{array}{l}
x \ge \sqrt 2 \\
x \le - \sqrt 2
\end{array} \right.\\
c)DK:4x - {x^2} - 5 \ge 0\\
\to - \left( {{x^2} - 4x + 5} \right) \ge 0\\
\to {x^2} - 4x + 5 \le 0\left( {vô lý} \right)\\
\to x \in \emptyset \\
d)DK:1 - 4{x^2} \ge 0\\
\to \dfrac{1}{2} \ge x \ge - \dfrac{1}{2}\\
e)DK: - 2{x^2} - 3x + 5 \ge 0\\
\to \left( {1 - x} \right)\left( {2x + 5} \right) \ge 0\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
1 - x \ge 0\\
2x + 5 \le 0
\end{array} \right.\\
\left\{ \begin{array}{l}
1 - x \le 0\\
2x + 5 \ge 0
\end{array} \right.
\end{array} \right. \to \left[ \begin{array}{l}
1 \ge x \ge - \dfrac{5}{2}\\
\left\{ \begin{array}{l}
1 \le x\\
x \ge - \dfrac{5}{2}
\end{array} \right.\left( l \right)
\end{array} \right.
\end{array}\)
