4)

a) $(x - 5)² - 49 = 0$

$(x-5)² = 49$

$x - 5 = ±7$

\(\left[ \begin{array}{l}x- 5=7\\x - 5=-7\end{array} \right.\) 

\(\left[ \begin{array}{l}x=12\\x=-2\end{array} \right.\) 

b) $(2x + 1)(1 - 2x) + (2x + 1)² = x$

$-(2x + 1)(2x-1) + (2x + 1)² - x = 0$

$-(4x² - 1) + 4x² - 4x + 1 - x = 0$

$-4x²+ 1 + 4x² - 4x + 1 - x = 0$

$-5x + 2 = 0$

$5x = 2$

$x = \dfrac{2}{5}$

c)

$(x-5)² + (x+3)(x-3) - 2(x+1)² = 0$

$x² - 10x + 25 + x² - 9 - 2(x² + 2x + 1) = 0$

$x² - 10x + 25 + x² - 9 - 2x² - 4x - 2 = 0$

$-14x + 14 = 0$

$14x = 14$

$x = 1$

Đáp án:

$\begin{array}{l}
3)a)M = 4x - {x^2} + 3\\
 =  - \left( {{x^2} - 4x + 4} \right) + 7\\
 =  - {\left( {x - 2} \right)^2} + 7 \le 7\\
 \Rightarrow GTLN:M = 7\,khi:x = 2\\
b)N = 2x - {x^2}\\
 =  - \left( {{x^2} - 2x} \right)\\
 =  - \left( {{x^2} - 2x + 1} \right) + 1\\
 =  - {\left( {x - 1} \right)^2} + 1 \le 1\\
 \Rightarrow GTLN:N = 1\,khi:x = 1\\
c)P = 2x - 2{x^2} - 5\\
 =  - 2\left( {{x^2} - x} \right) - 5\\
 =  - 2.\left( {{x^2} - 2.x.\frac{1}{2} + \frac{1}{4}} \right) + 2.\frac{1}{4} - 5\\
 =  - 2.{\left( {x - \frac{1}{2}} \right)^2} - \frac{9}{2} \le  - \frac{9}{2}\\
 \Rightarrow GTLN:P =  - \frac{9}{2}\,khi:x = \frac{1}{2}\\
4)\\
a){\left( {x - 5} \right)^2} - 49 = 0\\
 \Rightarrow {\left( {x - 5} \right)^2} = 49\\
 \Rightarrow \left[ \begin{array}{l}
x - 5 = 7\\
x - 5 =  - 7
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
x = 12\\
x =  - 2
\end{array} \right.\\
b)\left( {2x + 1} \right)\left( {1 - 2x} \right) + {\left( {2x - 1} \right)^2} = x\\
 \Rightarrow 1 - 4{x^2} + 4{x^2} - 4x + 1 = x\\
 \Rightarrow 5x = 2\\
 \Rightarrow x = \frac{2}{5}\\
c){\left( {x - 5} \right)^2} + \left( {x - 3} \right)\left( {x + 3} \right) - 2{\left( {x + 1} \right)^2} = 0\\
 \Rightarrow {x^2} - 10x + 25 + {x^2} - 9 - 2{x^2} - 4x - 2 = 0\\
 \Rightarrow  - 14x + 14 = 0\\
 \Rightarrow x = 1
\end{array}$