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