SOLUTION: if x-1/x=2 ,then x8+1/x8=?

Algebra ->  Sequences-and-series -> SOLUTION: if x-1/x=2 ,then x8+1/x8=?       Log On


   

Question 427260: if x-1/x=2 ,then x8+1/x8=?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We can square both sides to obtain

x%5E2+%2B+%281%2Fx%5E2%29+-+2+=+4 --> x%5E2+%2B+%281%2Fx%5E2%29+=+6. Square both sides again to get

x%5E4+%2B+%281%2Fx%5E4%29+%2B+2+=+36 --> x%5E4+%2B+%281%2Fx%5E4%29+=+34. Repeat.

x%5E8+%2B+%281%2Fx%5E8%29+%2B+2+=+1156, so x%5E8+%2B+%281%2Fx%5E8%29+=+1154.