\(a)\sqrt{3x+9}+\sqrt{x-4}=0\).
\(\Leftrightarrow\sqrt{3x+9}=-\sqrt{x-4}\\ \Leftrightarrow3x+9=x-4\\ \Leftrightarrow3x-x=-4-9\\ \Leftrightarrow2x=-13\\ \Leftrightarrow x=-\frac{13}{2}\left(KTM\right)\)
Thử lại không thỏa mãn
Vậy \(x\in\varnothing\)
\(b)\sqrt{4x^2+4x+1}+\sqrt{\left(x-3\right)^2}=0\).
\(\Leftrightarrow\sqrt{4x^2+4x+1}+\left|x-3\right|=0\\ \Leftrightarrow\sqrt{4x^2+4x+1}=-\left|x-3\right|\\ \Leftrightarrow\left\{{}\begin{matrix}\sqrt{4x^2+4x+1}=0\\-\left|x-3\right|=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\frac{1}{2}\left(KTM\right)\\x=3\left(KTM\right)\end{matrix}\right.\)
Thử lại cả hai giá trị đều không thỏa mãn
Vậy \(x\in\varnothing\)
\(c)\sqrt{x^2-4}+\sqrt{6-3x}=0\).
\(\Leftrightarrow\sqrt{x^2-4}=-\sqrt{6-3x}\\ \Leftrightarrow x^2-4=6-3x\\ \Leftrightarrow\left(x-2\right)\left(x+2\right)=3\left(2-x\right)\\ \Leftrightarrow\left(x-2\right)\left(x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\left(TM\right)\\x=-5\left(KTM\right)\end{matrix}\right.\)
Thử lại \(x=2\) thỏa mãn
