[(2)/(sqrt(4))+(3)/(sqrt(3))=2],[(4)/(sqrt(4))-(3)/(sqrt(9))=-1]

Solve: (2)/(sqrt(x))-(3)/(sqrt(y))=2 and (4)/(sqrt(x))-(9)/(sqrt(y))=-1

(2)/(sqrt(x))+(3)/(sqrt(y))=2 and (4)/(sqrt(x))-(9)/(sqrt(y))=-1

{:((2)/(sqrt(x))+ (3)/(sqrt(y)) = 2),((4)/(sqrt(x))-(9)/(sqrt(y)) = -1):}

(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2

(3sqrt(2))/(sqrt(6)-sqrt(3))+(2sqrt(3))/(sqrt(6)+2)-(4sqrt(3))/(sqrt(6)-sqrt(2))

The value of 6+log_((3)/(2))((1)/(3sqrt(2))sqrt(4-(1)/(3sqrt(2))sqrt(4-(1)/(3sqrt(2))sqrt(4-(1)/(3sqrt(2))...cdots))))

Prove that (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+....+(1)/(sqrt(8)+sqrt(9))=2