IV
1:
ĐKXĐ: \(x\in R\)
\(3\sqrt{x^2-3x+5}+2\left(x+1\right)\left(x-4\right)=9\)
=>\(3\sqrt{x^2-3x+5}+2\left(x^2-3x-4\right)=9\)
=>\(3\sqrt{x^2-3x+5}+2\left(x^2-3x+5-9\right)=9\)
=>\(2\left(x^2-3x+5\right)+3\sqrt{x^2-3x+5}-27=0\)
=>\(2\left(x^2-3x+5\right)+9\sqrt{x^2-3x+5}-6\sqrt{x^2-3x+5}-27=0\)
=>\(\sqrt{x^2-3x+5}\left(2\sqrt{x^2-3x+5}+9\right)-3\left(2\sqrt{x^2-3x+5}+9\right)=0\)
=>\(\left(2\sqrt{x^2-3x+5}+9\right)\left(\sqrt{x^2-3x+5}-3\right)=0\)
=>\(\sqrt{x^2-3x+5}-3=0\)
=>\(\sqrt{x^2-3x+5}=3\)
=>\(x^2-3x+5=9\)
=>\(x^2-3x-4=0\)
=>(x-4)(x+1)=0
=>\(\left[{}\begin{matrix}x-4=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-1\end{matrix}\right.\)
