Đáp án:
a) \(\left[ \begin{array}{l}
x = 0\\
x = 7
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a)7x - {x^2} = 0\\
\to x\left( {7 - x} \right) = 0\\
\to \left[ \begin{array}{l}
x = 0\\
7 - x = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 0\\
x = 7
\end{array} \right.\\
b)2{x^3} - 8{x^5} = 0\\
\to 2{x^3}\left( {1 - 4{x^2}} \right) = 0\\
\to \left[ \begin{array}{l}
x = 0\\
1 - 4{x^2} = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 0\\
{x^2} = \dfrac{1}{4}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 0\\
x = \dfrac{1}{2}\\
x = - \dfrac{1}{2}
\end{array} \right.\\
c)10n + 24 \vdots 2n + 3\\
\Leftrightarrow 5\left( {2n + 3} \right) + 9 \vdots 2n + 3\\
\Leftrightarrow 9 \vdots 2n + 3\\
\Leftrightarrow 2n + 3 \in U\left( 9 \right)\\
\to \left[ \begin{array}{l}
2n + 3 = 9\\
2n + 3 = 3\\
2n + 3 = 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
n = 3\\
n = 0\\
n = - 1
\end{array} \right.
\end{array}\)
