Question

If 3−√5/ 3+2√5 = a √5 - 19/ 11 , find a

Answer 1

3− (√5/ 3)+ (2√5) = a √5 - (19/ 11)

3− (√5/ 3)+ (2√5) + (19/ 11) = a √5

(3 + (19/11)) + ((√5/ 3)+ (2√5)) = a√5

(33+19)/11 + (√5+6√5)/3 = a√5

52/11 + 7√5/3 = a√5

(156 + 77√5)/33 = a√5

a = (156 + 77√5)/33√5