Question

已知x=根号2-1，y=根号2+1，求x\y+y\x的值

Answer 1

解：

设x\y+y\x=S

则S=(x²+y²)/xy

=[(x+y)²-2xy]/xy

=[(x+y)²/xy]-2

把x=√2 -1，y=√2 +1，代入得

S=6-2=4

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Answer 2

将已知的代入，得6

Answer 3

x/y+y/x=(x^2+y^2)/(xy)
=(x^2+y^2-2xy)/(xy)+2
=(x-y)^2/(xy)+2
xy=2-1=1,x-y=-2, x/y+y/x=6