[tex]\it ^{a)}a+\dfrac{1}{a}\ =\ ^{a)}5 \Rightarrow a^2+1=5a \Rightarrow a^2-5a+1=0|_{\cdot4} \Rightarrow\\ \\ \Rightarrow4a^2-20a+4=0 \Rightarrow 4a^2-20a+25-21=0\Rightarrow\\ \\ \Rightarrow (2a)^2-20a+5^2-(\sqrt{21})^2=0\Rightarrow(2a-5)^2-(\sqrt{21})^2=0\Rightarrow[/tex]
[tex]\it \Rightarrow (2a-5-\sqrt{21})(2a-5+\sqrt{21})=0 \Rightarrow \\ \\ \Rightarrow \begin{cases}\it 2a-5 - \sqrt{21}=0 \Rightarrow 2a=5+\sqrt{21}|_{:2}\Rightarrow a=\dfrac{5+\sqrt{21}}{2}\\ \\ \it 2a-5 + \sqrt{21}=0 \Rightarrow 2a=5-\sqrt{21}|_{:2}\Rightarrow a=\dfrac{5-\sqrt{21}}{2}\end{cases}[/tex]
