Đáp án:
$A = 1$
Giải thích các bước giải:
$\begin{array}{l}Ta\,\, có:\\ \dfrac{9}{4} - \sqrt5\\ = \dfrac{5}{4} - 2.\dfrac{\sqrt5}{2} + 1\\ = \left(\dfrac{\sqrt5}{2} - 1\right)^2\\ Tương\,\,tự:\\ \dfrac{9}{4} + \sqrt5\\ = \left(\dfrac{\sqrt5}{2} + 1\right)^2\\ Ta\,\,được:\\ x=9 - \dfrac{1}{\sqrt{\dfrac{9}{4} - \sqrt5}} + \dfrac{1}{\sqrt{\dfrac{9}{4} + \sqrt5}}\\ \Leftrightarrow x = 9 - \dfrac{1}{\dfrac{\sqrt5}{2} - 1} + \dfrac{1}{\dfrac{\sqrt5}{2} + 1}\\ \Leftrightarrow x = 9 - \left(\dfrac{2}{\sqrt5 - 2} - \dfrac{2}{\sqrt5 + 2}\right)\\ \Leftrightarrow x = 9 - 2\left[\dfrac{\sqrt5 + 2 - (\sqrt5 - 2)}{(\sqrt5 -2)(\sqrt5 + 2)}\right]\\ \Leftrightarrow x = 9 - 2.4\\ \Leftrightarrow x = 1\\ Do\,\,đó:\\ A = (x^4 - 3x + 1)^{2016} = (1^4 - 3.1 + 1)^{2016} = (-1)^{2016} = 1 \end{array}$
