`(sqrt(5)-1)/(sqrt(5)+1)+(sqrt(5)+1)/(sqrt(5)-1)`

If x=(sqrt(5)+1)/(sqrt(5)-1) and y=(sqrt(5)-1)/(sqrt(5)+1) find the value of x^(2)+y^(2)

If a=(sqrt(5)+1)/(sqrt(5)-1) and b=(sqrt(5)-1)/(sqrt(5)+1), the value of ((a^(2)+ab+b^(2))/(a^(2)-ab+b^(2))) is (3)/(4) (b) (4)/(3)(c)(3)/(5)(d)(5)/(3)

The value of (1)/(2)((sqrt(5)+1)/(1+sqrt(5)+sqrt(a))+(sqrt(5)-1)/(1-sqrt(5)+sqrt(a)))(sqrt(a)-(4)/(sqrt(a))+2)sqrt(0.002) is :

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

(1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5

(1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7))-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5