已知x^2-3x+1=0,求X^2+1/X^2的值

Question

已知x^2-3x+1=0,求X^2+1/X^2的值

Answer 1

因为x²-3x+1=0,所以x≠0
所以x²+1=3x
(x²+1)×1/x=3x×1/x
x+1/x=3
(x+1/x)²=3²
x²+1/x²+2×x×1/x=9
x²+1/x²+2=9
x²+1/x²=9-2=7
所以x²+1/x²=7