Question

If (5+2 √3/7+4√3) =a+b √3. then find the value of a and b​

Answer 1

Answer

7+4  

3

​

 

5+2  

3

​

 

​

=a+b  

3

​

 

Since rationalization of  

c+  

d

​

 

a+  

b

​

 

​

=  

c+  

d

​

 

a+  

b

​

 

​

×  

c−  

d

​

 

c−  

d

​

 

​

 

Taking L.H.S.

By rationalization,

7+4  

3

​

 

5+2  

3

​

 

​

 =  

7+4  

3

​

 

5+2  

3

​

 

​

×  

7−4  

3

​

 

7−4  

3

​

 

​

 

Since,   {(a+b)(a−b)=a  

2

−b  

2

}

           =  

[(7)  

2

−(4  

3

​

)  

2

]

(5+2  

3

​

)×(7−4  

3

​

)

​

         

           =  

49−16  

3

​

 

3

​

 

35+14  

3

​

−20  

3

​

−8  

3

​

 

3

​

 

​

 

           =  

49−48

35−  

3

​

(14−8)−24

​

 

           =  

1

35−  

3

​

(6)−24

​

 

           =11−6  

3

​

 

Hence, by comparing a = 11 & b = -6.