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

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