Question

Tìm x,thỏa mãn:

1)\(\sqrt{-x}\)=2

2)\(\sqrt{4x^2-4x+1}\)=3

Answer 1

1)

\(\sqrt{-x}=2\\ \Leftrightarrow\sqrt{-1.x}=2\\\Leftrightarrow \sqrt{-1.x}=\sqrt{4}\\ \Leftrightarrow-1.x=4\\ \Leftrightarrow x=-4\)

Vậy \(S=\left\{-4\right\}\)

\(2)\sqrt{4x^2-4x+1}=3\\\Leftrightarrow \sqrt{\left(2x-1\right)^2}=3\\\Leftrightarrow\left|2x-1\right| =3\\ \Leftrightarrow\left[{}\begin{matrix}2x-1=3\\2x-1=-3\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x=4\\2x=-2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=2\left(tm\right)\\x=-1\left(tm\right)\end{matrix}\right.\)

Vậy \(S=\left\{-1;2\right\}\)