Question

Find the value of a and b if (7 + 3sqrt(5))/(3 + sqrt(5)) + (7 - 3sqrt(5))/(3 - sqrt(5)) = a + sqrt(5) * b

Answer 1

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

(7 + 3√5)(3 - √5)/4 + (7 - 3√5)(3 + √5)/4 =

(21 + 2√5 - 15)/4 + (21 - 2√5 - 15)/4

6/4 + 6/4 = 3

a = 0, b = 3