Tìm x, biết : d) 25. (x + 1) ² - 16 = 0 e) 9. (x - 1) ² - (x+4) ² = 0 f) (2x - 1) ² = 9x ² + 12x + 4

Đáp án `+` Giải thích các bước giải:

`d)` `25(x+1)^2-16 = 0`

`<=> [5(x+1)]^2-4^2 = 0`

`<=> (5x+5)^2-4^2 = 0`

`<=> (5x+5-4)(5x+5+4) = 0`

`<=> (5x+1)(5x+9) = 0`

`<=>` \(\left[ \begin{array}{l}5x+1=0\\5x+9=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}5x=-1\\5x=-9\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=-\dfrac{1}{5}\\x=-\dfrac{9}{5}\end{array} \right.\) 

Vậy `x=-1/5` hoặc `x=-9/5`

`e)` `9(x-1)^2-(x+4)^2 = 0`

`<=> [3(x-1)]^2-(x+4)^2 = 0`

`<=> (3x-3)^2-(x+4)^2 = 0`

`<=> (3x-3-x-4)(3x-3+x+4) = 0`

`<=> (2x-7)(4x+1) = 0`

`<=>` \(\left[ \begin{array}{l}2x-7=0\\4x+1=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}2x=7\\4x=-1\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=\dfrac{7}{2}\\x=-\dfrac{1}{4}\end{array} \right.\) 

Vậy `x=7/2` hoặc `x=-1/4`

`f)` `(2x-1)^2 = 9x^2+12x+4`

`<=> (2x-1)^2 = (3x+2)^2`

`<=> (2x-1)^2-(3x+2)^2 = 0`

`<=> (2x-1-3x-2)(2x-1+3x+2) = 0`

`<=> (-x-3)(5x+1) = 0`

`<=>` \(\left[ \begin{array}{l}-x-3=0\\5x+1=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}-x=3\\5x=-1\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=-3\\x=-\dfrac{1}{5}\end{array} \right.\) 

Vậy `x=-3` hoặc `x=-1/5`