Đáp án:

\(\begin{array}{l}
1,\\
 - 1 < x < 1\\
2,\\
\left[ \begin{array}{l}
y \ge 3\\
y \le  - 2
\end{array} \right.
\end{array}\)

Giải thích các bước giải:

 Ta có:

\(\begin{array}{l}
1,\\
{x^4} + 4{x^2} - 5 < 0\\
 \Leftrightarrow \left( {{x^4} - {x^2}} \right) + \left( {5{x^2} - 5} \right) < 0\\
 \Leftrightarrow {x^2}.\left( {{x^2} - 1} \right) + 5.\left( {{x^2} - 1} \right) < 0\\
 \Leftrightarrow \left( {{x^2} - 1} \right)\left( {{x^2} + 5} \right) < 0\\
{x^2} \ge 0,\,\,\,\forall x \Rightarrow {x^2} + 5 \ge 5 > 0,\,\,\,\forall x\\
 \Rightarrow {x^2} - 1 < 0\\
 \Leftrightarrow {x^2} - {1^2} < 0\\
 \Leftrightarrow \left( {x - 1} \right)\left( {x + 1} \right) < 0\\
 \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x - 1 > 0\\
x + 1 < 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 1 < 0\\
x + 1 > 0
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x > 1\\
x <  - 1
\end{array} \right.\\
\left\{ \begin{array}{l}
x < 1\\
x >  - 1
\end{array} \right.
\end{array} \right. \Leftrightarrow  - 1 < x < 1\\
2,\\
{y^2} - y - 6 \ge 0\\
 \Leftrightarrow \left( {{y^2} - 3y} \right) + \left( {2y - 6} \right) \ge 0\\
 \Leftrightarrow y\left( {y - 3} \right) + 2.\left( {y - 3} \right) \ge 0\\
 \Leftrightarrow \left( {y - 3} \right)\left( {y + 2} \right) \ge 0\\
 \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
y - 3 \ge 0\\
y + 2 \ge 0
\end{array} \right.\\
\left\{ \begin{array}{l}
y - 3 \le 0\\
y + 2 \le 0
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
y \ge 3\\
y \ge  - 2
\end{array} \right.\\
\left\{ \begin{array}{l}
y \le 3\\
y \le  - 2
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
y \ge 3\\
y \le  - 2
\end{array} \right.
\end{array}\)