please prove you guys are the genius
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x+(1/x) = 2
(x²+1)/x = 2
x²+1 = 2x
x²-2x+1 = 0
x²-x-x+1 = 0
x(x-1)-1(x-1) = 0
(x-1)(x-1) = 0
x = 1. x = 1
x^5+(1/x^5) = 2
LHS = (1)^5+(1)^5/1^5
LHS = 1+1
LHS = 2
LHS = RHS
(x²+1)/x = 2
x²+1 = 2x
x²-2x+1 = 0
x²-x-x+1 = 0
x(x-1)-1(x-1) = 0
(x-1)(x-1) = 0
x = 1. x = 1
x^5+(1/x^5) = 2
LHS = (1)^5+(1)^5/1^5
LHS = 1+1
LHS = 2
LHS = RHS
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