(5x-6).(6x+9)-x^2.(6-5x)=0 tìm x giùm em nha 19/07/2021 Bởi Katherine (5x-6).(6x+9)-x^2.(6-5x)=0 tìm x giùm em nha
Đáp án: \[\left[ \begin{array}{l}x = \dfrac{6}{5}\\x = – 3\end{array} \right.\] Giải thích các bước giải: Ta có: \(\begin{array}{l}\left( {5x – 6} \right)\left( {6x + 9} \right) – {x^2}\left( {6 – 5x} \right) = 0\\ \Leftrightarrow \left( {5x – 6} \right).\left( {6x + 9} \right) – {x^2}.\left[ { – \left( {5x – 6} \right)} \right] = 0\\ \Leftrightarrow \left( {5x – 6} \right).\left( {6x + 9} \right) + {x^2}.\left( {5x – 6} \right) = 0\\ \Leftrightarrow \left( {5x – 6} \right)\left( {6x + 9 + {x^2}} \right) = 0\\ \Leftrightarrow \left( {5x – 6} \right){\left( {x + 3} \right)^2} = 0\\ \Leftrightarrow \left[ \begin{array}{l}5x – 6 = 0\\{\left( {x + 3} \right)^2} = 0\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \dfrac{6}{5}\\x = – 3\end{array} \right.\end{array}\) Bình luận
Đáp án:
\[\left[ \begin{array}{l}
x = \dfrac{6}{5}\\
x = – 3
\end{array} \right.\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\left( {5x – 6} \right)\left( {6x + 9} \right) – {x^2}\left( {6 – 5x} \right) = 0\\
\Leftrightarrow \left( {5x – 6} \right).\left( {6x + 9} \right) – {x^2}.\left[ { – \left( {5x – 6} \right)} \right] = 0\\
\Leftrightarrow \left( {5x – 6} \right).\left( {6x + 9} \right) + {x^2}.\left( {5x – 6} \right) = 0\\
\Leftrightarrow \left( {5x – 6} \right)\left( {6x + 9 + {x^2}} \right) = 0\\
\Leftrightarrow \left( {5x – 6} \right){\left( {x + 3} \right)^2} = 0\\
\Leftrightarrow \left[ \begin{array}{l}
5x – 6 = 0\\
{\left( {x + 3} \right)^2} = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{6}{5}\\
x = – 3
\end{array} \right.
\end{array}\)