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
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
等于 三个字
答
X^1/2＋X^-1/2＝3
即：（x+1）/（x^(1/2)）=3
平方一下有（x^2+2x+1）/x=9;即X^-1＋X＝9-2=7
同样的方法：X^2＋X^-2＝47
第三问不晓得你的÷管到哪个地方，你应该加上括号。
答
解: 1)x^(-1)+x=[x^(1/2)+x^(-1/2)]^2-2
=9-2=7
2)x^2+x^(-2)=[x^(-1)+x]^2-2
=49-2=47
3)[x^(3/2)-x^(-3/2)]/[x^(1/2)-x^(-1/2)]
=x+1+x^(-1)
=8.
答
1.17/4
2.257/16
3.75/8
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