\(\Leftrightarrow\sqrt{x-3-2\cdot\sqrt{x-3}\cdot3+9}=1\)
\(\Leftrightarrow\left|\sqrt{x-3}-3\right|=1\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-3}-3=-1\\\sqrt{x-3}-3=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-3=4\\x-3=16\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=19\end{matrix}\right.\)
`x + 6 - 6sqrt(x-3) =1`
`-> 6 sqrt(x-3) = x - 5`
`-> 6x - 18 = x^2 -10x + 25`
`-> x^2 - 16x + 33 = 0`
`\Delta = 124.`
`-> x = (16 +-sqrt 124)/2`
`-> x = 8 +-sqrt 31.`
đk x >= 3
\(\sqrt{x-3-6\sqrt{x-3}+9}=1\Leftrightarrow\left|\sqrt{x-3}-3\right|=1\)
\(\left[{}\begin{matrix}\sqrt{x-3}=4\\\sqrt{x-3}=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=19\\x=7\end{matrix}\right.\left(tm\right)\)
⇔√x−3−2⋅√x−3⋅3+9=1⇔x−3−2⋅x−3⋅3+9=1
⇔∣∣√x−3−3∣∣=1⇔|x−3−3|=1
⇔[√x−3−3=−1√x−3−3=1⇔[x−3=4x−3=16⇔[x=7x=19
