SOLUTION: If (x + 1/x) = 1 and (z + 1/z) =1; show that (z + 1/x) =1

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Question 464084: If (x + 1/x) = 1 and (z + 1/z) =1; show that (z + 1/x) =1
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
As it stands, the statement is not true.
Let +x%3C%3Ez+. Then both x and z are the roots of the quadratic equation x%5E2+-+x+%2B+1+=+0, and both roots are complex. Hence one root is the complex conjugate of the other, by theorem in algebra.
Also from algebra, xz = 1.
==> z = 1/x.
==> z+%2B+1%2Fx+=+1%2Fx+%2B+1%2Fx+=+2%2Fx+%3C%3E1+, since 2/x would be a (non-real) complex number.