a: \(\Leftrightarrow\sqrt{5x-3}\left(\sqrt{5x+3}-2\right)=0\)
=>5x-3=0 hoặc 5x+3=4
=>x=3/5 hoặc x=1/5
b: \(\Leftrightarrow\sqrt{x-5}+2\sqrt{x-5}-\dfrac{1}{5}\cdot3\sqrt{x-5}=3\)
\(\Leftrightarrow2.4\sqrt{x-5}=3\)
=>x-5=25/16
hay x=105/16
`a)\sqrt{25x^2-9}-2\sqrt{5x-3}=0` `ĐK: x >= 3/5`
`<=>\sqrt{(5x-3)(5x+3)}-2\sqrt{5x-3}=0`
`<=>\sqrt{5x-3}(\sqrt{5x+3}-2)=0`
`<=>` $\left[\begin{matrix}\sqrt{5x-3}=0\\ \sqrt{5x+3}=2\end{matrix}\right.$
`<=>` $\left[\begin{matrix} 5x-3=0\\ 5x+3=4\end{matrix}\right.$
`<=>` $\left[\begin{matrix} x=\dfrac{3}{5} (t/m)\\ x=\dfrac{1}{5} (ko t/m)\end{matrix}\right.$
Vậy `S={3/5}`
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`b)\sqrt{x-5}+\sqrt{4x-20}-1/5\sqrt{9x-45}=0` `ĐK: x >= 5`
`<=>\sqrt{x-5}+2\sqrt{x-5}-3/5\sqrt{x-5}=0`
`<=>12/5\sqrt{x-5}=0`
`<=>\sqrt{x-5}=0`
`<=>x-5=0`
`<=>x=5` (t/m)
Vậy `S={5}`
\(\sqrt{25x^2-9}-2\sqrt{5x-3}=0\left(ĐK:x>=\dfrac{3}{5}\right)\\ < =>\sqrt{\left(5x-3\right)\left(5x+3\right)}-2\sqrt{5x-3}=0\\ < =>\sqrt{5x-3}\left(\sqrt{5x+3}-2\right)=0\\ =>\left[{}\begin{matrix}\sqrt{5x-3}=0\\\sqrt{5x+3}-2=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}5x-3=0\\5x+3=4\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=\dfrac{3}{5}\left(TMDK\right)\\x=\dfrac{1}{5}\left(KTMDK\right)\end{matrix}\right.=>x=\dfrac{3}{5}\)
\(\sqrt{x-5}+\sqrt{4x-20}-\dfrac{1}{5}\sqrt{9x-45}=3\left(ĐK:x>=5\right)\\ < =>\sqrt{x-5}+\sqrt{4}.\sqrt{x-5}-\dfrac{1}{5}.\sqrt{9}.\sqrt{x-5}=3\\ < =>\left(1+2-\dfrac{3}{5}\right).\sqrt{x-5}=3\\ < =>\dfrac{12}{5}.\sqrt{x-5}=3\\ < =>\sqrt{x-5}=\dfrac{5}{4}\\ < =>x-5=\dfrac{25}{16}\\ < =>x=\dfrac{105}{16}\left(TMDK\right)\)
