Find the value of `a` and `b.`
`{4+sqrt 2}/{2+sqrt 2}=a-sqrt b`

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

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

find the value of ( 3 + sqrt3 ) xx ( 2 + sqrt2 )

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

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

Find the values of a and b in each of the (sqrt(7)-2)/(sqrt(7)+2)= a sqrt(7)+b

Using binomial theorem, write the value of (a+b)^(6) + (a-b)^(6) and hence find the value of ( sqrt(3) + sqrt(2) )^(6) + ( sqrt(3) - sqrt(2) )^(6) .

Find the value of x in sqrt(x+2sqrt(x+2sqrt(x+2sqrt(3x))))...=x.

Suppose a ,b, and c are in A.P. and a^2, b^2 and c^2 are in G.P. If a

(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)) .