Find the value of `x` and `y.`
`{5+sqrt 6}/{5-sqrt 6} =x+y sqrt 6`

(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)) .

Find the value of the following log_((5+2sqrt6)) (5-2sqrt6)

(2) Find a and b if (5-sqrt6)/(5+sqrt6) =a+bsqrt 6

If t a ntheta=-1/(sqrt(5)) and theta lies in the IV quadrant, then the value of costheta is a. (sqrt(5))/(sqrt(6)) b. 2/(sqrt(6)) c. 1/2 d. 1/(sqrt(6))

Find the value of 6/(sqrt(5)-\ sqrt(3)) , it being given that sqrt(3)=1. 732\ \ a n d\ \ sqrt(5)=2. 236

Let k be a real number such that the inequality sqrt(x-3) +sqrt(6 -x) ge k has a solution then the maximum value of k is sqrt3 (2) sqrt6 -sqrt3 (3) sqrt6 (4) sqrt6 +sqrt3

Find x and y if: (3/sqrt(5) x-5)+i2 sqrt (5) y= sqrt(2)

Multiply 6sqrt(5) by 2sqrt(5) .

Let f(x ,y)=x y^2 if xa n dy satisfy x^2+y^2=9 then the minimum value of f(x ,y) is 0 (2) -3sqrt(3) -6sqrt(3) (4) -3sqrt(6)

Find the values of a and b in each of the following : (a)(5+2sqrt3)/(7+4sqrt(3))=a-6sqrt(3)" "(b)(3-sqrt(5))/(3+2sqrt(5))=asqrt(5)-(19)/(11) (c )(sqrt(2)+sqrt(3))/(3sqrt2-2sqrt(3))=2-bsqrt(6)" "(d)(7+sqrt(5))/(7-sqrt(5))-(7-sqrt(5))/(7+sqrt(5))=a+(7)/(11)sqrt(5b)