SOLUTION: please help me to solve. if f(x)=7 show that x^2-√ 5x-1=0 where f(x)=(1+x^4+x^8)/x^8

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Question 1047617: please help me to solve.
if f(x)=7 show that x^2-√ 5x-1=0 where f(x)=(1+x^4+x^8)/x^8
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
please help me to solve.
if f(x)=7 show that x^2-sqrt(5)x-1=0 where f(x)=(1+x^4+x^8)/x^8
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You are given

%281%2Bx%5E4%2Bx%5E8%29%2Fx%5E8 = 7.

Then

1%2Fx%5E8 + 1%2Fx%5E4 + 1 = 7,  or

1%2Fx%5E8 + 1%2Fx%5E4 - 6 = 0.

Factor the left side

%28%281%2Fx%5E4%29+%2B3%29%2A%28%281%2Fx%5E4%29-2%29 = 0,  which gives the roots

x%5E4 = -1%2F3   and   x%5E4 = 1%2F2.

OK, I just pointed the way for you.

At this point I leave you.

If you can, please complete the analysis on your own.

I do not think that the original statement is correct, but have no any desire to prove or disprove it.