Đáp án:
a. \(\left[ \begin{array}{l}
x = 8\\
x = - 5
\end{array} \right.\)
b. \(\left[ \begin{array}{l}
x = - \frac{3}{2}\\
x = 4
\end{array} \right.\)
c. \(\left[ \begin{array}{l}
x = \frac{{ - 3 + \sqrt {21} }}{2}\\
x = \frac{{ - 3 - \sqrt {21} }}{2}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a){\left( {x - 5} \right)^2} + 7x = 65\\
\to {x^2} - 10x + 25 + 7x = 65\\
\to {x^2} - 3x - 40 = 0\\
\to {x^2} - 8x + 5x - 40 = 0\\
\to x\left( {x - 8} \right) + 5\left( {x - 8} \right) = 0\\
\to \left( {x - 8} \right)\left( {x + 5} \right) = 0\\
\to \left[ \begin{array}{l}
x = 8\\
x = - 5
\end{array} \right.\\
b)\left( {2x + 3} \right)\left( {2x--3} \right) = 5\left( {2x + 3} \right)\\
\to \left( {2x + 3} \right)\left( {2x - 3 - 5} \right) = 0\\
\to \left[ \begin{array}{l}
2x + 3 = 0\\
2x - 8 = 0
\end{array} \right. \to \left[ \begin{array}{l}
x = - \frac{3}{2}\\
x = 4
\end{array} \right.\\
c)3x\left( {x--2} \right)--5\left( {{x^2} + 1} \right) = --11\\
\to 3{x^2} - 6x - 5{x^2} - 5 + 11 = 0\\
\to - 2{x^2} - 6x + 6 = 0\\
\to \left[ \begin{array}{l}
x = \frac{{ - 3 + \sqrt {21} }}{2}\\
x = \frac{{ - 3 - \sqrt {21} }}{2}
\end{array} \right.
\end{array}\)
