Question

giải phương tình

3)\(\sqrt{4\left(x-1\right)^2=8}\)

Answer 1

=>\(\sqrt{2^2\left(x-1\right)^2}=8\)

=>2(x-1)=8

=>x-1=4

=>x=5

Answer 2

\(\sqrt{4\left(x-2\right)^2}=8\)

<=> \(\sqrt{2^2\left(x-2\right)^2}=\sqrt{64}\)

<=> 2²(x - 2)² = 64

<=> 4(x² - 4x + 4) = 64

<=> 4x² - 16x + 16 = 64

<=> 4x² - 16x + 16 - 64 = 0

<=> 4x² - 16x - 48 = 0

<=> 4x² + 8x - 24x - 48 = 0

<=> 4x(x + 2) - 24(x + 2) = 0

<=> (4x - 24)(x + 2) = 0

<=> 4(x - 6)(x + 2) = 0

<=> \(\left[{}\begin{matrix}x-6=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-2\end{matrix}\right.\)