Question

Find a,b
(5+√3) / (√5-√3) = (1/2)a+3b√15

Answer 1

Answer:

a = 5√5 + 5√3 + 3

b = 1 / 6

Step-by-step explanation:

( 5 + √3 ) / ( √5 - √3 ) = a / 2 + 3b√15

Rationalising the denominator

=> { ( 5 + √3 )( √5 + √3 ) } / { ( √5 - √3 )( √5 + √3 ) } = a / 2 + 3b√15

=> ( 5√5 + 5√3 + √15 + 3 ) / 2 = a / 2 + 3b√15

=> ( 5√5 + 5√3 + 3 + √15 ) / 2 = a / 2 + 3b√15

=> ( 5√5 + 5√3 + 3 ) / 2 + √15 / 2 = a / 2 + 3b√15

Comparing on both sides

• => a = 5√5 + 5√3 + 3

• => √15 / 2 = 3b√15

=> 1 / 2 = 3b

=> 1 / 6 = b