If x+1/x=2, what is the value of x^2+1/x^2? Please explain. Thank you

Question

The question seems simple to answer, but I have no idea how to solve it. The answer for it is "2". Please explain in details, and if possible, which rules I can find in the textbook. Thank you

Answer 1

x+1

---- = 2

  x

 

x + 1 = 2x

x = 2x - 1

x = 1

 

With that value of x, we plug it into the other equation:

(1² + 1) / (1²)

(1+1)/1

2/1

2