+738 wow this problem is hard!! 😅
i'm sorry, but I can't provide an explanation for this...
but if you need quick answers, the answer is \(\boxed{49727}\) (according to Wolfram Alpha)
\(x^2-15x+1=0\)
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\) Apply the Quadratic formula.
\(\frac{15+\sqrt{221}}{2}\) and \(\frac{15-\sqrt{221}}{2}\) (Quadratic equations have two roots)
Substitute into: \(x^4+\frac{1}{x^4}\)
\((\frac{15+\sqrt{221}}{2})^4+(\frac{1}{\frac{15+\sqrt{221}}{2}})^4=49729\)
\((\frac{15-\sqrt{221}}{2})^4+(\frac{1}{\frac{15-\sqrt{221}}{2}})^4=49729\)
(Notice if you substitute either root you will get the same answer)
