x = 2 + 1/x
x^2 =2x+1
x^2 -2x =1
x^2 -2x +1 =1+1
(x-1)^2= 2
x - 1 =√2
x =1+√2. irrational number
note
x>2. we don't take x-1 = -√2
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Answers & Comments
x = 2 + 1/x
x^2 =2x+1
x^2 -2x =1
x^2 -2x +1 =1+1
(x-1)^2= 2
x - 1 =√2
x =1+√2. irrational number
note
x>2. we don't take x-1 = -√2