\(A=x^2-x+\dfrac{1}{x}+2015\\ =\left(x^2-2x+1\right)+\left(x+\dfrac{1}{x}\right)+2014\\ =\left(x-1\right)^2+\left(x+\dfrac{1}{x}\right)+2014\ge2\sqrt{x\cdot\dfrac{1}{x}}+2014=2016\)
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