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[x - 1/x]^2 = x^2 + 1/x^2 - 2.x.1/x
x^2 + 1/x^2 = [x-1/x]^2 + 2.x.1/x
x^2 + 1/x^2 = 81+2
x^2 + 1/x^2 = 83
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