Question

\(\sqrt{x}+2=\left|x-4\right|\)

Answer 1

ĐKXĐ: \(x\ge0\)

\(\sqrt{x}+2=\left|x-4\right|\\\Leftrightarrow \left[{}\begin{matrix}\sqrt{x}+2=x-4\\\sqrt{x}+2=4-x\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x-\sqrt{x}-6=0\\x+\sqrt{x}-2=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)=0\\\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=3\left(vì\sqrt{x}\ge0\right)\\\sqrt{x}=1\left(vì\sqrt{x}\ge0\right)\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=9\left(tm\right)\\x=1\left(tm\right)\end{matrix}\right.\)

Answer 2

th1

nếu 4>=x thì

căn x +2=4-x

=> căn x +2 =(2-căn x).(2+ căn x)

rút gọn còn 0=2-căn x

=>căn x=2

=>x=4

 

th2 x>4 bạn Cm tương tự nhé