1.
x-y=3
y=(根号10)-3
(1/(y-x))+y=(1/3)+(根号10)-3=(根号10)+(8/3)
((1/(y-x))+y)^2=10+(64/9)+(16/3)(根号10)=(154/9)+(16/3)(根号10)
((1/(y-x))+y)^(2/3)=((154/9)+(16/3)(根号10))^(1/3)
2.
x^(1/2)+x^(-1/2)=3 ----------(A)
两边平方：
x+x^(-1)+2=9
x+x^(-1)=7
(A)式两边立方：
x^(3/2)+3x*x^(-1/2)+3x^(1/2)*x^(-1)+x^(-3/2)=27
x^(3/2)+x^(-3/2)+3(x^(1/2)+x^(-1/2))=27
x^(3/2)+x^(-3/2)=27-3*7=6
所以：
x的二分之三方+x的负二分之三方+2/x的负一次方+x+3
=(x^(3/2)+x^(-3/2)+2)/(x^(-1)+x+3)
=(6+2)/(7+3)=4/5