If both of a and b are rational numbers, find the values of a and b in each of the following equalities:
          (i)     (ii) (iii)
        (iv) 

(i)   -1 is the conjugate surd of  +1
   
   
       
        
         2 - =  a + b 
      Hence, a = 2 ,  b = -1 

 (ii)  is the conjugate of 3-

=
=
=
On comparing both sides
         
We have a =  and b =
 (iii) 7-4 is the conjugate of 7 + 4
            ∴      
                  =    
                                   = 
                               = 35 -20
On comparing both sides
        
11-6
We have,   a = 11,  b = -6.
(iv)  is the conjugate of the denominator 3