Question

7 + 3 root 5 by 3 + root 5 = a+b root 5

Answer 1

7+3 root 5by 3+ root 5 minus 7-3 root 5 by 3- root 5 = a+ root 5 b find the value of a and b

(7 + 3√5)/(3 + √5)  -   (7 - 3√5)/(3 - √5)  = a + b√5

LHS

= (7 + 3√5)/(3 + √5)  -   (7 - 3√5)/(3 - √5)

= ( (7 + 3√5)(3 - √5)  - (7 - 3√5)(3 + √5) ) / ( 3² - √5²)

= (21 + 2√5 - 15 - (21 -2√5 -15) ) / ( 9 - 5)

= 4√5 / 4

= √5

= 0  + 1 *√5

Comparing with RHS

a + b√5

a = 0

b = 1