1.
[tex]6a+\dfrac{1}{a}=5\\\\ 6a^2+1=5a\\ 6a^2-5a+1=0\\ 6a^2-3a-2a+1=0\\ 3a(2a-1)-1(2a-1)=0\\ (3a-1)(2a-1)=0\\ a=\dfrac{1}{3} \vee a=\dfrac{1}{2}[/tex]
2.
[tex]3a-\dfrac{1}{a}=2\\\\ 3a^2-1=2a\\ 3a^2-2a-1=0\\ 3a^2-3a+a-1=0\\ 3a(a-1)+1(a-1)=0\\ (3a+1)(a-1)=0\\ a=-\dfrac{1}{3} \vee a=1[/tex]
3.
[tex]4a+\dfrac{1}{a}=-5\\ 4a^2+1=-5a\\ 4a^2+5a+1=0\\ 4a^2+4a+a+1=0\\ 4a(a+1)+1(a+1)=0\\ (4a+1)(a+1)=0\\ a=-\dfrac{1}{4} \vee a=-1[/tex]
