Question

Z + 1/z = 2 ; z = (?)

Answer 1

Z + 1/z = 2
Multiply 1 by both sides
z+z=2
Add z and z together
2z=2
Divide both sides by 2
Final Answer: z= 1

Answer 2

$z + \dfrac{1}{z} = 2$ 

$\text{Multiply both sides by the common denominator z}$ 

$z^2+1=2z$ 

$\text{Move all terms to one side}$ 

$z^2+1-2z=0$

$z^2+1-2z$ $\text{fits the form}$ $a^2-2ab+b^2$ 

$\text{Rewrite it where a=z and b=1}$ 

$z^2-2(z)(1)+12=0$ 

$\text{Use Square of Difference}$ $(a-b)^2=a^2-2ab+b^2$ 

$(z-1)^2=0$ 

$\text{Take the square root of both sides}$ 

$z-1=0$ 

$\text{Add 1 to both sides}$ 

$\text{Solution ----- \ }z=1$