Question

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

Answer 1

`z + (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`

Answer 2

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