已知x^(1/2)+x^(-1/2)=3求（x^2+x^-2-2)/(x^(3/2)+x^(-3/2)-3的值我只知道分子有个平分和分母有个立方和但约不了分好奇怪啊

Question

已知x^(1/2) +x^(-1/2)=3 求（x^2+x^-2 -2)/(x^(3/2)+x^(-3/2)-3的值
我只知道分子有个平分和 分母有个立方和 但约不了分好奇怪啊

Answer 1

x^1/2 +x^(-1/2) =3
两边平方
x+2+x^(-1)=9
x+x^(-1)=7
两边平方
x^2+2+x^(-2)=49
x^2+x^(-2)=47
x^(3/2)+x^(-3/2)立方和公式
=[x^1/2 +x^(-1/2)][x-x^1/2*x^(-1/2)+x^(-1)]
=3*(7-1)
=18
所以(x^2+x^(-2)-2)/(x^(3/2)+x^(-3/2)-3)
=(47-2)/(18-3)
=3