Question

Answer 1

a. \(\sqrt{3x-1}=5\)

<=> 3x - 1 = 5²

<=> 3x = 25 + 1

<=> 3x = 26

<=> x = \(\dfrac{26}{3}\)

b. \(\sqrt{\left(x-2\right)^2}=2x-1\)

<=> \(|x-2|=2x-1\)

<=> \(\left[{}\begin{matrix}x-2=2x-1\\x-2=-\left(2x-1\right)\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=1\\x-2=-2x+1\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=1\\-x=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)