\(\sqrt{4x^2-9}=2\sqrt{2x+3}\left(đk:x\ge-\dfrac{3}{2}\right)\)
\(\Rightarrow\sqrt{\left(2x\right)^2-3^2}=2\sqrt{2x+3}\)
\(\Rightarrow\sqrt{\left(2x-3\right).\left(2x+3\right)}-2\sqrt{2x+3}=0\)
\(\Rightarrow\sqrt{2x+3}.\left(\sqrt{2x-3}-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2x+3=0\\\sqrt{2x-3}=2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\left(tm\right)\\x=\dfrac{7}{2}\left(tm\right)\end{matrix}\right.\)
\(\sqrt{9-4x^2}=5\sqrt{3-2x}\left(đk:x\le\dfrac{3}{2}\right)\)
\(\Rightarrow\sqrt{3^2-\left(2x\right)^2}=5\sqrt{3-2x}\)
\(\Rightarrow\sqrt{\left(3-2x\right)\left(3+2x\right)}-5\sqrt{3-2x}=0\)
\(\Rightarrow\sqrt{3-2x}.\left(\sqrt{3+2x}-5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}3-2x=0\\\sqrt{3+2x}=5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\left(tm\right)\\x=11\left(l\right)\end{matrix}\right.\)
\(\sqrt{x-2}-3\sqrt{x^2-4}=0\) (đk: x>= 2)
\(\Rightarrow\sqrt{x-2}-3\sqrt{x^2-2^2}=0\)
\(\Rightarrow\sqrt{x-2}-3\sqrt{\left(x-2\right).\left(x+2\right)}=0\)
\(\Rightarrow\sqrt{x-2}.\left(1-3\sqrt{x+2}\right)\)=0
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\3\sqrt{x+2}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\x=-\dfrac{17}{9}\left(l\right)\end{matrix}\right.\)
\(\sqrt{4x^2-9}=2\sqrt{2x+3}Đk:x\ge-\dfrac{3}{2}\)
\(\Rightarrow\sqrt{\left(2x\right)^2-3^2}=2\sqrt{2x+3}\)
\(\Rightarrow\)\(\sqrt{\left(2x-3\right).\left(2x+3\right)}=2\sqrt{2x+3}\)
\(\Rightarrow\sqrt{2x-3}=2\)
\(\Rightarrow2x-3=4\)
\(\Rightarrow2x=7\)
\(\Rightarrow x=\dfrac{7}{2}\)(t/m)
