Question

若x2-3x+1=0,则x2/x4+x2+1的值为

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Answer 1

x^2-3x+1 = 0

x^2/(x^4+x^2+1)
[(x^2-3x+1) + (3x-1)]/ [x^2(x^2-3x+1) + 3x^3+1]
=(3x-1)/(3x^3+1)
=(3x-1)/[3x(x^2-3x+1) +9x^2-3x+1]
= (3x-1)/(9x^2-3x+1)
= (3x-1)/[9(x^2-3x+1) + 24x-8)
=(3x-1)/[8(3x-1)]
=1/8