Question

Find the value of a and b if 7+ root 5/7-root 5 = a+b root5 /11

Answer 1

7+rt5/7-rt5
Rationalizing the denominator:
(7+root 5) * (7 + root 5)/ (7- root 5)*(7 + root 5)
= (7+root 5 )^2/ (49 - 5)
= 49 + 5 + 2*7*root 5 / 44
= 54 + 14*root5 / 44
Given, the result = (a + b*root5)/11
(a+b root 5)/11 = (54 + 14 root5)/44
Comapring:
a/11 = 54/44
a = 54*11/44 = 27/2
b root 5/11 = 14 root5/44
b = 11*14/44 = 7/2
Hence, a = 27/2 or 13.5 && b = 7/2 or 3.5 
Hope it helps.