Question

\(x-4\sqrt{x-2}+1=0\)

Answer 1

ĐK:....

\(x-4\sqrt{x-2}+1=0\)

\(\Leftrightarrow x-2-4\sqrt{x-2}+4-1=0\)

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

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x-2=9\\x-2=1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=11\\x=3\end{matrix}\right.\)( thỏa )

Vậy....

Answer 2

\(x-4\sqrt{x-2}+1=0\)

\(\Leftrightarrow\left(x-2\right)-4\sqrt{x-2}+4-1=0\)

\(\Leftrightarrow\left(\sqrt{x-2}-2\right)^2-1^2=0\)

\(\Leftrightarrow\left(\sqrt{x-2}-1\right)\left(\sqrt{x-2}-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-2}-1=0\\\sqrt{x-2}-3=0\end{matrix}\right.\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x-2=1\\x-2=9\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=11\end{matrix}\right.\)

Vậy nghiệm của phương trình là \(x=\left\{3;11\right\}\)

Answer 3