a) \(\left(x-\sqrt{2}\right)+3\left(x^2-2\right)=0\)
\(\Leftrightarrow\left(x-\sqrt{2}\right)+3\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
\(\Leftrightarrow\left(x-\sqrt{2}\right)\left[3\left(x+\sqrt{2}\right)+1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}x-\sqrt{2}=0\\3x+3\sqrt{2}+1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\sqrt{2}\\3x=-3\sqrt{2}-1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\sqrt{2}\\x=\frac{-3\sqrt{2}-1}{3}\end{matrix}\right.\)
Vậy phương trình có tập nghiệm S={\(\sqrt{2};\frac{-3\sqrt{2}-1}{3}\)}
b) \(x^2-5=\left(2x-\sqrt{5}\right)\left(x+\sqrt{5}\right)\)
\(\Leftrightarrow\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)=\left(2x-\sqrt{5}\right)\left(x+\sqrt{5}\right)\)
\(\Leftrightarrow\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)-\left(2x-\sqrt{5}\right)\left(x+\sqrt{5}\right)=0\)
\(\Leftrightarrow\left(x+\sqrt{5}\right)\left(x-\sqrt{5}-2x+\sqrt{5}\right)\)
\(\Leftrightarrow\left(x+\sqrt{5}\right)\times x=0\)
\(\Rightarrow\left[{}\begin{matrix}x+\sqrt{5}=0\\x=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=-\sqrt{5}\\x=0\end{matrix}\right.\)
Vậy phương trình có tập nghiệm S={\(0;-\sqrt{5}\)}
