Question 1047617
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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

{{{(1+x^4+x^8)/x^8}}} = 7.

Then

{{{1/x^8}}} + {{{1/x^4}}} + {{{1}}} = 7,  or

{{{1/x^8}}} + {{{1/x^4}}} - {{{6}}} = 0.

Factor the left side

{{{((1/x^4) +3)*((1/x^4)-2)}}} = 0,  which gives the roots

{{{x^4}}} = {{{-1/3}}}   and   {{{x^4}}} = {{{1/2}}}.

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.
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