Đề bài
Giải các phương trình sau:
a] \[2{x^2} + 3x = 0\]
b] \[{x^2} - 2x - 15 = 0\]
c] \[4{x^2} - 9 = 0\]
Lời giải chi tiết
\[\begin{array}{l}a]\;2{x^2} + 3x = 0\\ \Leftrightarrow x\left[ {2x + 3} \right] = 0\\ \Leftrightarrow \left[ \begin{array}{l}x = 0\\2x + 3 = 0\end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l}x = 0\\x = - \dfrac{3}{2}\end{array} \right.\end{array}\]
\[\begin{array}{l}b]\;{x^2} - 2x - 15 = 0\\ \Leftrightarrow {x^2} - 5x + 3x - 15 = 0\\ \Leftrightarrow x\left[ {x - 5} \right] + 3\left[ {x - 5} \right] = 0\\ \Leftrightarrow \left[ {x - 5} \right]\left[ {x + 3} \right] = 0\\ \Leftrightarrow \left[ \begin{array}{l}x - 5 = 0\\x + 3 = 0\end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l}x = 5\\x = - 3\end{array} \right.\end{array}\]
\[\begin{array}{l}c]\;4{x^2} - 9 = 0\\ \Leftrightarrow {\left[ {2x} \right]^2} - {3^2} = 0\\ \Leftrightarrow \left[ {2x - 3} \right].\left[ {2x + 3} \right] = 0\\ \Leftrightarrow \left[ \begin{array}{l}2x - 3 = 0\\2x + 3 = 0\end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l}x = \dfrac{3}{2}\\x = - \dfrac{3}{2}\end{array} \right.\end{array}\]