Đáp án:
\(\begin{array}{l}
1)x = - \dfrac{5}{2}\\
3)x = \dfrac{5}{4}\\
5)x = \dfrac{{15}}{8}\\
7)x \in \emptyset \\
9)x = - \dfrac{3}{2}\\
4)x = - \dfrac{{12}}{{11}}\\
6)x = \dfrac{{38}}{9}\\
8)x = \dfrac{1}{4}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
1){x^2} - x - 20 - {x^2} + 11x = 5\\
\to 10x = 25\\
\to x = \dfrac{5}{2}\\
3)2{x^2} - 8x + 2x = 2{x^2} + 6x - 20 + 5\\
\to 12x = 15\\
\to x = \dfrac{5}{4}\\
5){x^2} - 9x + 20 - {x^2} + x + 2 = 7\\
\to - 8x = - 15\\
\to x = \dfrac{{15}}{8}\\
7)2{x^2} - x - 2{x^2} + x + 6 = 0\\
\to 6 = 0\left( l \right)\\
\to x \in \emptyset \\
9){x^2} - 6x + 5 = {x^2} - 3x + 2 + 3x + 12\\
\to - 6x = 9\\
\to x = - \dfrac{3}{2}\\
2)4{x^3} + 12{x^2} - x - 3 - 4{x^3} - 2{x^2} + 2x + 1 = {x^2}\\
\to 9{x^2} + x - 2 = 0\\
\to \left[ \begin{array}{l}
x = \dfrac{{ - 1 + \sqrt {73} }}{{18}}\\
x = \dfrac{{ - 1 - \sqrt {73} }}{{18}}
\end{array} \right.\\
4)6{x^2} + x - 15 + 3 = 6{x^2} + 12x\\
\to 11x = - 12\\
\to x = - \dfrac{{12}}{{11}}\\
6)6\left( {{x^2} + x - 12} \right) - 6{x^2} + 12x - 4 = 0\\
\to 6{x^2} + 6x - 72 - 6{x^2} + 12x - 4 = 0\\
\to 18x = 76\\
\to x = \dfrac{{38}}{9}\\
8)4{x^2} + 7x - 2 - 7x = 4{x^2} + 6x - 2x - 3\\
\to 4x = 1\\
\to x = \dfrac{1}{4}
\end{array}\)
