Question

已知x²--6x+1=0，求x²+1/x²的值

急，请大家帮个忙

Answer 1

∵x^2-6x+1=0
∴x^2=6x-1
∴x^2+1/x^2=6x-1+1/(6x-1)
进行通分合并得
x^2+1/x^2
=(36x^2-12x+2)/(6x-1)=(34x^2+2x^2-6x+2)/x^2
∵2x^2-6x+2=2(x^2-6x+1)=0
∴x^2+1/x^2=34x^2/x^2=34
∴答案为34

Answer 2

∵x^2-6x+1=0
∴x^2=6x-1
∴x^2+1/x^2=6x-1+1/(6x-1)
进行通分合并得
x^2+1/x^2
=(36x^2-12x+2)/(6x-1)=(34x^2+2x^2-6x+2)/x^2
∵2x^2-6x+2=2(x^2-6x+1)=0
∴x^2+1/x^2=34x^2/x^2=34
∴答案34 这是一楼写的，有一个小错误(34x^2+2x^2-6x+2)/x^2 应该是(34x^2+2x^2-12x+2)/x^2，∵2x^2-6x+2=2(x^2-6x+1)=0应该是2x^2-12x+2=2(x^2-6x+1)=0，望改正

Answer 3

M=b²-4ac=36-4=32
x=6+_4根号2/2=3+_2根号2
x²+1/x²=6/x=6(3+_2根号2)