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
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![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](/uploads/image/z/7214121-9-1.jpg?t=%E8%A7%A3%E4%B8%80%E9%81%93%E6%8C%87%E6%95%B0%E5%87%BD%E6%95%B0%E7%9A%84%E9%A2%98%21%E5%B7%B2%E7%9F%A5X%5E1%2F2%EF%BC%8BX%5E-1%2F2%EF%BC%9D3%281%29X%5E-1%EF%BC%8BX%EF%BC%9D%282%29X%5E2%EF%BC%8BX%5E-2%EF%BC%9D%283%29X%5E3%2F2%EF%BC%8DX%5E-3%2F2%C3%B7X%5E1%2F2%EF%BC%8DX%5E-1%2F2)
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
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
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
(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
1.17/4
2.257/16
3.75/8
等于 三个字
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。
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.