Question

giải pt

\(\sqrt{x^2-4x+4}\)=3

Answer 1

\(\sqrt{x^2-4x+4}=3\)

`<=> x^2 -4x +4 = 9`

`<=> x^2 -4x +4 -9 =0`

`<=> x^2 -4x -5 =0`

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

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

Vậy `S={-1;5}`

Answer 2

`\sqrt{x^2-4x+4}=3`

`<=>\sqrt{(x-2)^2}=3`

`<=>|x-2|=3`

`<=>` $\left[\begin{matrix} x-2=3\\ x-2=-3\end{matrix}\right.$

`<=>` $\left[\begin{matrix} x=5\\ x=-1\end{matrix}\right.$

Vậy `S={-1;5}`

Answer 3

\(\Leftrightarrow\sqrt{\left(x-2\right)^2}=3\)

\(\Leftrightarrow\left|x-2\right|=3\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=3\\2-x=3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)