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x is a root of x^2 - 15x + 1 = 0.  Find x^4 + 1/x^4.

 May 4, 2020
 #1
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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)

 May 4, 2020
 #2
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\(x^2-15x+1=0\)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\) 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)

 May 4, 2020

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