a)\(\sqrt{\left(x-3\right)^2}=3-x\)Đk \(x\ge3\)
\(\Leftrightarrow\left|x-3\right|=3-x\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=3-x\\x-3=x-3\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(nhận\right)\\0=0\left(vôlý\right)\end{matrix}\right.\)
Vậy S=\(\left\{3\right\}\)
b)\(x^2-7=0\)
\(\Leftrightarrow\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{7}\\x=-\sqrt{7}\end{matrix}\right.\)
Vậy S=\(\left\{\sqrt{7},-\sqrt{7}\right\}\)
c)\(x^2-2\sqrt{2}x+2=0\)
\(\Leftrightarrow\left(x-\sqrt{2}\right)^2=0\)
\(\Leftrightarrow x=\sqrt{2}\)
Vậy S=\(\left\{\sqrt{2}\right\}\)
d)\(\sqrt{x^2-16x+64}=5\)đk \(x\ge8\)
\(\Leftrightarrow\sqrt{\left(x-8\right)^2}=5\)
\(\Leftrightarrow\left|x-8\right|=5\)
\(\Leftrightarrow\left[{}\begin{matrix}x-8=5\\x-8=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=13\left(nhận\right)\\x=3\left(loại\right)\end{matrix}\right.\)
Vây S=\(\left\{13\right\}\)
