急.数学指数运算..设x>0,若x^(1/2) + x^(-1/2) =3,求[x^2+(x^-2) -2] / [x^(3/2)_数学解答

急.数学指数运算.
.设x>0,若x^(1/2) + x^(-1/2) =3,求[x^2+(x^-2) -2] / [x^(3/2) +x^(-3/2)-3]

人气：240 ℃　时间：2020-05-08 17:04:35

解答

[x^(1/2)+ x^(-1/2)]^2 =(x+x^-1)+2=9x+x^-1=7 x+x^=8
[x^(1/2)+ x^(-1/2)]^3=x^(3/2) +x^(-3/2)+3[x^(1/2)+ x^(-1/2)]=x^(3/2) +x^(-3/2)+9
原式=(x+x^-1)^2-4/[x^(1/2)+ x^(-1/2)]^3-12=60/15=4