Đáp án:
$\begin{array}{l}
B3)a)Dkxd:{x^2} + 1 \ge 0\\
\Leftrightarrow {x^2} \ge - 1\left( {tm} \right)\\
\text{Vậy biểu thức xác định với mọi x}\\
b)Dkxd:4{x^2} + 3 \ge 0\\
\Leftrightarrow 4{x^2} \ge - 3\left( {tm} \right)\\
\text{Vậy biểu thức xác định với mọi x}\\
c)Dkxd:9{x^2} - 6x + 1 \ge 0\\
\Leftrightarrow {\left( {3x - 1} \right)^2} \ge 0\left( {tm} \right)\\
\text{Vậy biểu thức xác định với mọi x}\\
d)Dkxd: - {x^2} + 2x - 1 \ge 0\\
\Leftrightarrow {x^2} - 2x + 1 \le 0\\
\Leftrightarrow {\left( {x - 1} \right)^2} \le 0\\
Do:{\left( {x - 1} \right)^2} \ge 0\\
\Leftrightarrow x - 1 = 0\\
\Leftrightarrow x = 1\\
\text{Vậy}\,x = 1\\
e)Dkxd: - \left| {x + 5} \right| \ge 0\\
\Leftrightarrow \left| {x + 5} \right| \le 0\\
\Leftrightarrow x + 5 = 0\\
\Leftrightarrow x = - 5\\
\text{Vậy}\,x = - 5\\
f)Dkxd: - 2{x^2} - 1 \ge 0\\
\Leftrightarrow 2{x^2} \le - 1\left( {ktm} \right)\\
\text{Vậy}\,x \in \emptyset \\
B4)\\
a)Dkxd:4 - {x^2} \ge 0\\
\Leftrightarrow {x^2} \le 4\\
\Leftrightarrow - 2 \le x \le 2\\
\text{Vậy}\, - 2 \le x \le 2\\
b)Dkxd:{x^2} - 16 \ge 0\\
\Leftrightarrow {x^2} \ge 16\\
\Leftrightarrow \left[ \begin{array}{l}
x \ge 4\\
x \le - 4
\end{array} \right.\\
\text{Vậy}\,x \le - 4\,\text{hoặc}\,x \ge 4\\
c)Dkxd:{x^2} - 3 \ge 0\\
\Leftrightarrow {x^2} \ge 3\\
\Leftrightarrow \left[ \begin{array}{l}
x \ge \sqrt 3 \\
x \le - \sqrt 3
\end{array} \right.\\
\text{Vậy}\,x \le - \sqrt 3 \,\text{hoặc}\,x \ge \sqrt 3 \\
d)Dkxd:{x^2} - 2x - 3 \ge 0\\
\Leftrightarrow \left( {x - 3} \right)\left( {x + 1} \right) \ge 0\\
\Leftrightarrow \left[ \begin{array}{l}
x \ge 3\\
x \le - 1
\end{array} \right.\\
\text{Vậy}\,x \le - 1\,\text{hoặc}\,x \ge 3\\
e)Dkxd:x\left( {x + 2} \right) \ge 0\\
\Leftrightarrow \left[ \begin{array}{l}
x \ge 0\\
x \le - 2
\end{array} \right.\\
\text{Vậy}\,x \le - 2\,\text{hoặc}\,x \ge 0\\
f)Dkxd:{x^2} - 5x + 6 \ge 0\\
\Leftrightarrow \left( {x - 2} \right)\left( {x - 3} \right) \ge 0\\
\Leftrightarrow \left[ \begin{array}{l}
x \ge 3\\
x \le 2
\end{array} \right.\\
\text{Vậy}\,x \le 2\,\text{hoặc}\,x \ge 3
\end{array}$
