If x + 1/x =2,then find x^10+1/x^10

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Solution

x + 1/x = 2
=> 1/x = 2 - x
=> 1 = 2x - x^2
=>x^2 - 2x + 1 = 0
=> (x - 1) ^2 = 0
=> (x - 1) = 0
=> x = 1

So we have x^10+1/x^10 = 1^10 + 1/1^10 = 2

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