Question

己知:x+x分之一=3,求:x^2+x^2分之一,x^4+x^2+1分之x^2,(x-x分之一)^2的值

Answer 1

1.∵x+1/x=3
∴(x+1/x)^2=9
x^2+2+1/x^2=9
x^2+1/x^2=9-2=7
2.题目应该是x^4+x^2+1/x^2
=x^4+2x^2+1/x^2-x^2
即(x^2+1/x^2)^2-x^2=49-x^2
∵x^2+1/x^2=7
∴原式=x^4+7
∴49-x^2=x^4+7
x^4+x^2-42=0
设x^2=y,x^4=y^2
y^2+y-42=0
(y-6)(y+7)=0
y1=6,y2=-7舍去
∴x=±√6
∴原式=49-(±√6)^2=43
3.∵x^2+2+1/x^2=9(题目1)即x^2+1/x^2=7
又∵(x-1/x)^2=x^2-2+1/x^2,7代入得7-2=5

追问

谢谢

Answer 2

x^2+x^2分之一
=(x+1/x)^2-2
=3^2-2
=7

(x-x分之一)^2
=x^2+1/x^2 -2
=7-2
= 5

中间那题看不清分子分母

Answer 3

7 ？？ 5