a) \(\sqrt{25x^2}=100\)
\(25x^2=10000\)
\(x^2=400\)
\(x=\pm20\)
b) \(\left(\sqrt{3}-\sqrt{2}\right)x=\sqrt{27}-\sqrt{18}\)
\(\left(\sqrt{3}-\sqrt{2}\right)x=\sqrt{9.3}-\sqrt{9.2}\)
\(\left(\sqrt{3}-\sqrt{2}\right)x=3\left(\sqrt{3}-\sqrt{2}\right)\)
\(x=3\)
a. \(\sqrt{25x^2}=100\)
\(\Leftrightarrow\sqrt{\left(5x\right)^2}=100\)
\(\Leftrightarrow\left|5x\right|=100\)
\(\Leftrightarrow\left[{}\begin{matrix}5x=100\\5x=-100\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=20\\x=-20\end{matrix}\right.\)
b. \(\left(\sqrt{3}-\sqrt{2}\right)x=\sqrt{27}-\sqrt{18}\)
\(\Leftrightarrow\left(\sqrt{3}-\sqrt{2}\right)x=\sqrt{3^2.3}-\sqrt{3^2.2}\)
\(\Leftrightarrow\left(\sqrt{3}-\sqrt{2}\right)x=3\sqrt{3}-3\sqrt{2}\)
\(\Leftrightarrow\left(\sqrt{3}-\sqrt{2}\right)x=3\left(\sqrt{3}-\sqrt{2}\right)\)
\(\Leftrightarrow x=3\)