x(x-1)(x+1)(x-2)+1=0怎么解?

2025-04-30 22:13:33
推荐回答(3个)
回答1:

令y=(x+1)(x-2)
则函数是个开口向上的抛物线,与x轴的交点是(-1,0)和(2,0)
∴当y>0时,即抛物线在x轴的上方
则x<-1或x>2

回答2:

(x²-x)(x²-x-2)+1=0
(x²-x)²-2(x²-x)+1=0
(x²-x-1)²=0
x²-x+1/4=1+1/4=5/4
(x-1/2)²=5/4
x=1/2±√5/2

回答3:

x(x-1)(x+1)(x-2)+1=0
(x²-x)(x²-x-2)+1=0
(x²-x)²-2(x²-x)+1=0
(x²-x-1)²=0
x²-x-1=0
x²-x+1/4=1+1/4
(x-1/2)²=5/4
x=(1±√5)/2