Question

۱۱۰ If a = 9-4√5, -then find the value of a-1÷a​

Answer 1

- 8 - 4root5

Explanation:

`a - 1 ÷ a = (9 - 4 √(5)) - 1 / (9 - 4 √(5)) \\ = (8 - 4 √(5))/(9 - 4 √(5) ) \\ = (8 - 4 √(5))/(9 - 4 √(5)) * (9 + 4 √(5))/(9 + 4 √(5)) \\ = \frac{(8 - 4 √(5))(9 + 4 √(5)) }{9 {}^(2) - 4 √(5) \: {}^(2) } \\ = (72 + 32 √(5) \: - 36 √(5) \: - 80)/(81 - 80) \\ = ( - 8 - 4 √(5) )/(1) \\ = - 4 \: ( \: 2 + √(5) \: )`