Question

Please answer quickly ​

Answer 1

`(4+3\sqrt 5)/(4-3\sqrt 5)\\\\\\=(\left(4+3\sqrt 5 \right)\left(4+3\sqrt 5 \right))/(\left(4-3\sqrt 5 \right)\left(4+3\sqrt 5 \right)) \\\\\\=(\left(4+3\sqrt 5 \right)^2)/(4^2 - \left( 3 \sqrt 5 \right)^2)\\\\\\=(4^2 + 2\cdot 4 \cdot 3\sqrt 5 + \left( 3\sqrt 5 \right)^2)/(16-9\cdot 5)\\\\\\=(16+24\sqrt 5 + 45)/(16-45)\\\\\\=(61+24\sqrt5)/(-29)\\\\\\=-(61)/(29)-(24)/(29)\sqrt 5\\\\\\=-\left((61)/(29)\right) + \left(- (24)/(29) \right) \sqrt 5`

`\text{It is now in a form of}~ a+b\sqrt 5~, \text{where}\\ \\a=-(61)/(29)~~ \text{and}~~ b =- (24)/(29)`