\(6\sqrt{x-2}+5\sqrt{x-2}-4\sqrt{x-2}=14\)
\(7\sqrt{x-2}=14\Leftrightarrow\sqrt{x-2}=2\)
\(\left\{{}\begin{matrix}2>0\left(luondung\right)\\x-2=4\end{matrix}\right.\)\(\Leftrightarrow x=6\left(tm\right)\)
\(\sqrt{\left(2\sqrt{3}-4\right)^2}-\sqrt{19-8\sqrt{3}}=\left|2\sqrt{3}-4\right|-\sqrt{\left(4-\sqrt{3}\right)^2}=4-2\sqrt{3}-\left|4-\sqrt{3}\right|=4-\sqrt{3}-4+\sqrt{3}=-\sqrt{3}\)
\(\dfrac{\sqrt{21}+\sqrt{15}}{\sqrt{7}+\sqrt{5}}-\dfrac{15}{\sqrt{5}}+\dfrac{6}{\sqrt{7}-\sqrt{5}}=\sqrt{3}-3\sqrt{5}+3\sqrt{7}+3\sqrt{5}==\sqrt{3}+3\sqrt{7}\)
ĐKXĐ: \(x\ge2\)
\(3\sqrt{4x-8}+\sqrt{25x-50}-\sqrt{16x-32}=14\)
\(\Rightarrow3\sqrt{4\left(x-2\right)}+\sqrt{25\left(x-2\right)}-\sqrt{16\left(x-2\right)}=14\)
\(\Rightarrow6\sqrt{\left(x-2\right)}+5\sqrt{\left(x-2\right)}-4\sqrt{\left(x-2\right)}=14\)
\(\Rightarrow7\sqrt{\left(x-2\right)}=14\)
\(\Rightarrow\sqrt{\left(x-2\right)}=2\)
\(\Rightarrow x-2=4\)
\(\Rightarrow x=6\)
\(\sqrt{4x^2-8x+4}-1=5\\ \Rightarrow\sqrt{4\left(x-1\right)^2}-1=5\\ \Rightarrow2\left|x-1\right|=6\\ \Rightarrow\left|x-1\right|=3\\ \Rightarrow\left[{}\begin{matrix}x-1=-3\\x-1=3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-2\\x=4\end{matrix}\right.\)
