x - 1/x = 8

squaring on both sides

(x-1/x) ^ 2 = 8 ^ 2 = 64

x^2 + 1/x^2 - 2.x.1/x = 64

x^2 + 1/x^2 = 64+2 = 66 ----- (1)

(x + 1/x)^2 = x^2 + 1/x^2 + 2.x.1/x

= 66 + 2 =68

x+1/x = √68 = 8.246

hope this helps ❤️

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