\(\left(x^4+x^3-x^2+1\right)^2+2016=\left(x^2\left(x^2+x-1\right)+1\right)+2016\left(1\right)\)
Ta có: \(x^2+x-1=\left(\dfrac{\sqrt{5}-1}{2}\right)^2+\dfrac{\sqrt{5}-1}{2}-1
=\dfrac{5-2\sqrt{5}+1}{4}+\dfrac{2\sqrt{5}-2}{4}-\dfrac{4}{4}=0.\) Khi đó ta có: (1) \(\Leftrightarrow\left[x^2.0+1\right]^2+2016=1^2+2016=2017.\)
Vậy với \(x=\dfrac{\sqrt{5}-1}{2}\)thì (x4 + x3 - x2 + 1)2 + 2016 = 2017.