if x^2-5x+1=0 them x^2+1/x^2
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x1,2=12(5±21−−√)
Now since x2=5x−1 and x1=1/x2 we have
x2+1x2=52(5+21−−√)−1+52(5−21−−√)−1=25−2=23.
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