已知x+(1/x)=3,求(1)x²+(1/x²);(2)(x-1/x)² .
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/12 00:46:10
![已知x+(1/x)=3,求(1)x²+(1/x²);(2)(x-1/x)² .](/uploads/image/z/1143863-71-3.jpg?t=%E5%B7%B2%E7%9F%A5x%2B%281%2Fx%29%3D3%2C%E6%B1%82%EF%BC%881%EF%BC%89x%26%23178%3B%2B%281%2Fx%26%23178%3B%29%EF%BC%9B%EF%BC%882%EF%BC%89%EF%BC%88x-1%2Fx%EF%BC%89%26%23178%3B+.)
xTJ0~ sf*6{B@r!UW0*LwM7
$ҹ+Ki|9%r=s.w+nCT# 0y `1eZXN/'bx9}p3G xac1l2HaLUQK1I By'EK_./Xl9S
m BwŊU
C_*!622%tKVؠs{v={-H߰BaD¨(Qri$d
jAl!In:;n~7ȯ7\},_;0"yl(%[E s`I|]d'o`4yK xTN&h
>KƤD$ů
w;ݛ
qw!gl\۫6y:픴/4kJ]_*h4>=6Tǧ+LnTp=
2')@H^\Yr$
f
已知x+(1/x)=3,求(1)x²+(1/x²);(2)(x-1/x)² .
已知x+(1/x)=3,求(1)x²+(1/x²);(2)(x-1/x)² .
已知x+(1/x)=3,求(1)x²+(1/x²);(2)(x-1/x)² .
x+(1/x)=3
[x+(1/x)]²=3²
x²+2+(1/x²)=9
∴x²+1/x²=7
(2)(x-1/x)²
(x-1/x)²
=x²-2+1/x²
=7-2
=5
(x+1/x)²=9
(1)
x²+1/x²=(x+1/x)²-2=7
(2)
(x-1/x)²=x²+1/x²-2=5
(1)x²+(1/x²)=(x+1/x)²-2=7
(2)(x-1/x)²=x²+(1/x²)-2=7-2=5
两边同时*1/x
1+1/x²=3
1/x²=2
x²=1/2
(1)原式=1/2+2=5/2
(2)原式=x²-2+1/x²=1/2
我回答错了,不想改了嘿嘿!
﹙1﹚∵x+﹙1/3﹚=3 ∴x²+﹙1/x²﹚=﹙x+1/x﹚²-2x﹙1/x﹚=9-2=7.
﹙2﹚∵﹙x-1/x﹚²=x²+﹙1/x﹚²-2x﹙1/x﹚=﹙x+1/x﹚²-4x﹙1/x﹚=9-4=5。
很简单,多动动脑子就行了,祝你学习愉快。
(1)、∵x+(1/x)=3 ∴[x+(1/x)]²=x²+﹙1/x﹚²+2=9,∴x²+(1/x²)=7
(2)、(x-1/x)² =x²-2+(1/x)²,∵x²+(1/x²)=7,∴x²-2+(1/x)²=5,即(x-1/x)² =5