[tex]z + \dfrac{1}{z} = 2[/tex]
[tex]\text{Multiply both sides by the common denominator z}[/tex]
[tex]z^2+1=2z
[/tex]
[tex]\text{Move all terms to one side}[/tex]
[tex]z^2+1-2z=0
[/tex]
[tex]z^2+1-2z[/tex] [tex]\text{fits the form}[/tex] [tex]a^2-2ab+b^2[/tex]
[tex]\text{Rewrite it where a=z and b=1}[/tex]
[tex]z^2-2(z)(1)+12=0
[/tex]
[tex]\text{Use Square of Difference}[/tex] [tex](a-b)^2=a^2-2ab+b^2
[/tex]
[tex](z-1)^2=0
[/tex]
[tex]\text{Take the square root of both sides}[/tex]
[tex]z-1=0[/tex]
[tex]\text{Add 1 to both sides}[/tex]
[tex]\text{Solution ----- \ }z=1[/tex]
