解一道指数函数的题!
问题描述：
解一道指数函数的题!
已知X^1/2＋X^-1/2＝3
(1)X^-1＋X＝
(2)X^2＋X^-2＝
(3)X^3/2－X^-3/2÷X^1/2－X^-1/2
答
(1)
(X^1/2＋X^-1/2)^2＝9
X^-1＋X+2=9
X^-1＋X=7
(2)
(X^-1＋X)^2=49
X^2＋X^(-2)+2=49
X^2＋X^-2=47
(3)
(X^2＋X^-2)(X^-1＋X)
=X^3+X^(-3)+X+1/X
=X^3+X^(-3)+7=329
X^3+X^(-3)=322
(X^3/2－X^-3/2)÷(X^1/2－X^-1/2)
={[X^3+X^(-3)-2]/[X^-1＋X-2]}^1/2
=(320/5)^1/2
=8