+0

# help

0
44
2

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

May 4, 2020

#1
+457
0

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
0

$$x^2-15x+1=0$$

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