Find values of `a` and `b` when `(sqrt(2)-1)/(sqrt(2)+1)=a+b sqrt(2)`

(1+sqrt(2))/(3-2sqrt(2))=A sqrt(2)+B

Find the values of a and b if (6)/(3sqrt(2)-2sqrt(3))=a sqrt(2)-b sqrt(3)

Find the values of a and b in each of the (5+3sqrt(2))/(5-3sqrt(2))= a+b sqrt(2)

12.Rationalise and find the value of' "a'" and "'b'" ; (i) "(sqrt(3)-1)/(sqrt(3)+1)=a+b sqrt(3), (ii) (sqrt(5)-2)/(sqrt(5)+2)=a+b sqrt(5)

find the value (sqrt(2)+7)/(sqrt(2)-1)+sqrt(8)

find the value (sqrt(2)+7)/(sqrt(2)-1)+sqrt(8)

Find the value of a and b . (sqrt11 - sqrt7 ) / (sqrt 11 + sqrt 7) = a - b sqrt 77 (i) a = 9/2 , b = 1/2 (ii) a = 2/9, b = 2/3 (iii) a = 2/5, b = 1/2 (iv) a = 9/2, b =5/2

(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 (sqrt(a + 2b) + sqrt(a - 2b))/(sqrt(a + 2b) - sqrt(a - 2b)) = sqrt3 and a^(2) + b^(2) = 1 , then the find values of a and b. (b) If sqrt((x - sqrt(a^(2) - b^(2)))^(2) + y^(2)) + sqrt((x + sqrt(a^(2) - b^(2)))^(2) + y^(2)) = 2a then prove that (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1