若x^1\2+x^-1\2=3,求分子x^3\2+x^-3\2-3\分母x^2+x^-2-2的值
问题描述：
若x^1\2+x^-1\2=3,求分子x^3\2+x^-3\2-3\分母x^2+x^-2-2的值
答
∵x（1/2）+x(-1/2)=3
∴x+1/x+2=9,
x+1/x=7
∵x（3/2）+x(-2/3)
=[x（1/2）+x(-1/2)](x-1+1/x)
=3*{[x（1/2）+x(-1/2)]^2-2-1}
=3*{9-2-1}
=18
x(2)+x(-2)=(x+1/x)^-2=49-2=47
∴原式=(18-3)/(47-2)=15/45=1/3