" If "((sqrt(3)+1))/((sqrt(3)-1))=a+b sqrt(3)," find the values of "a" and "b

If a=(sqrt(3)+1)/(sqrt(3)-1) and b=(sqrt(3)-1)/(sqrt(3)+1) ,find the value of a^(2)+ab-b^(2)

If x = (sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) , find the value of x^(3) + (1)/(x^(3)) .

(i) If x = (6ab)/(a + b) , find the value of : (x + 3a)/(x - 3a) + (x + 3b)/(x - 3b) . (ii) a = (4sqrt(6))/(sqrt(2) + sqrt(3)) , find the value of : (a + 2sqrt(2))/(a - 2sqrt(2)) + (a + 2sqrt(3))/(a - 2sqrt(3)) .

If a=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) and b=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)), find the value of a^(2)+ab+b^(2)

If a = (1)/(2 - sqrt(3)) , b = (1)/(2 + sqrt(3)) , find the value of ((a + b)/(a -b))^(2) .

(sqrt(2)+sqrt(3))/(3sqrt(2)-2sqrt(3))=2-b sqrt(6) find b

if a,b are coprime numbers and satisfying (2+sqrt(3))^(((1-sqrt(3)))/(log_(a)(2-sqrt(3)))+(13-1)/(sqrt(3)+1))=(1)/(12) then find the value of (a+b)

If a=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and b=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) , then find the value of 3(a^(2)-b^(2)) .