SOLUTION: Given that (alpha) is the root of the equation x^2= 2x-1, show that: (a) (alpha)^3= 3(alpha) -2 , (b) (alpha)^4-(alpha)^2= 2(alpha)-2

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Question 173565: Given that (alpha) is the root of the equation x^2= 2x-1, show that:
(a) (alpha)^3= 3(alpha) -2 ,
(b) (alpha)^4-(alpha)^2= 2(alpha)-2
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2=2x-1 → x%5E2-2x%2B1=0 → %28x-1%29%5E2=0 → x=1, therefore alpha=1

(a) alpha%5E3=1%5E3=1 and 3%2Aalpha+-+2+=+3%2A1+-+2+=+1

(b) alpha%5E4-alpha%5E2=1%5E4-1%5E2=1-1=0 and 2%2Aalpha+-+2=+2%2A1-2=+0