已知x＾2分之一次方+x＾负二分之一次方=3,求x＾二分之三+x＾负二分之三-3分之x＾2+x＾-2-2的值.一定要正确啊

Question

已知x＾2分之一次方+x＾负二分之一次方=3,求x＾二分之三+x＾负二分之三-3分之x＾2+x＾-2-2的值.一定要正确啊

Answer 1

x^(1/2)+x^(-1/2)=3
[x^(1/2)+x^(-1/2)]^2=9
x+x^(-1)+2=9
x+x^(-1)=7
(x+x^(-1))^2=49
x^2+x^(-2)+2=49
x^2+x^(-2)=47
3分之(x＾2+x＾-2-2)=(47-2)/3=15
x^(3/2)+x^(-3/2)
=(x^(1/2)+x^(-1/2))(x+x^(-1)-1)
=3*(7-1)
=18
x＾二分之三+x＾负二分之三-3分之x＾2+x＾-2-2
=18-15
=3