Đáp án:
a) \(\left[ \begin{array}{l}
x = 15\\
x = - 9
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a)48 + 288:{\left( {x - 3} \right)^2} = 50\\
\to 288:{\left( {x - 3} \right)^2} = 2\\
\to {\left( {x - 3} \right)^2} = 144\\
\to \left| {x - 3} \right| = 12\\
\to \left[ \begin{array}{l}
x - 3 = 12\\
x - 3 = - 12
\end{array} \right. \to \left[ \begin{array}{l}
x = 15\\
x = - 9
\end{array} \right.\\
b)x - \left[ {x - \left( {x + x - 1} \right)} \right] = 1\\
\to x - \left( {x - 2x + 1} \right) = 1\\
\to x + x - 1 = 1\\
\to 2x = 2\\
\to x = 1\\
c)x\left( {x - 3} \right) = 0\\
\to \left[ \begin{array}{l}
x = 0\\
x = 3
\end{array} \right.\\
d)x\left( {x - 3} \right) < 0\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x > 0\\
x - 3 < 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x < 0\\
x - 3 > 0
\end{array} \right.
\end{array} \right. \to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x > 0\\
x < 3
\end{array} \right.\\
\left\{ \begin{array}{l}
x < 0\\
x > 3
\end{array} \right.\left( l \right)
\end{array} \right.\\
e)\left( {x - 3} \right)\left( {6 - x} \right) > 0\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x - 3 > 0\\
6 - x > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 3 < 0\\
6 - x < 0
\end{array} \right.
\end{array} \right. \to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x > 3\\
6 > x
\end{array} \right.\\
\left\{ \begin{array}{l}
x < 3\\
x > 6
\end{array} \right.\left( l \right)
\end{array} \right.\\
f)\left| {x - 3} \right| = 7\\
\to \left[ \begin{array}{l}
x - 3 = 7\\
x - 3 = - 7
\end{array} \right. \to \left[ \begin{array}{l}
x = 10\\
x = - 4
\end{array} \right.\\
g)\left| {x - 5} \right| = x + 3\\
\to \left[ \begin{array}{l}
x - 5 = x + 3\\
x - 5 = - x - 3
\end{array} \right.\\
\to \left[ \begin{array}{l}
- 5 = 3\left( l \right)\\
2x = 2
\end{array} \right.\\
\to x = 1
\end{array}\)
