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
来源:学生作业帮助网 编辑:六六作业网 时间:2024/08/25 08:40:05
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.