Question

Giải các phương trình: 

a) (\(x^2-4x\))\(^2\) = 4\(\left(x^2-4x\right)\) 

b) \(\left(x+2\right)^2-x+1=\left(x-1\right)\left(x+1\right)\)  

Answer 1

a) (x² - 4x)² = 4(x² - 4x) 

<=> (x² - 4x)(x² - 4x - 4) = 0

<=> x(x - 4)(x² - 4x - 4) = 0

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\\left(x-2\right)^2=8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=\pm\sqrt{8}+2\end{matrix}\right.\)

b) (x + 2)² - x + 1 = (x - 1)(x + 1) 

<=> x² + 4x + 4 - x + 1 = x² - 1

<=> 3x + 5 = -1

<=> x = -2