Question

已知X²-3X+1=0 求下列各式的值 (1)x² +x²分之1 （2）x³+x

Answer 1

(1)

xx-3x+1=0

=>

x+1/x = 3

=>

xx + 1/xx = (x+1/x)^2 - 2 = 7

(2)

xxx+1/xxx = (1/x + x )(xx+1/xx) - (1/x + x) = 7*3-3=18

(3)

xxxxx+1/xxxxx = (1/xx+xx)(xxx+1/xxx) - (1/x+x) = 18*7-3=123