Question

若x^(1/2)-x(-1/2)=3.求[x^(3/2)-x(-3/2)-3]/[x^2+x^(-2)-2]的值

Answer 1

（X^(1/2)-X^(-1/2))^3=27

X^(3/2)-3X^(1/2)+3X^(-1/2)-X^(-3/2)=27

x^(3/2)-x^(-3/2)-3=33;

（X^(1/2)-X^(-1/2))^2=9

X-2+X^(-1)=9

(X+X^(-1))^2=121

X^2+X^(-2)-2=117

因此：[X^(3/2)-X(-3/2)-3]/[X^2+X^(-2)-2]=3861