Question

7 + 3√5 7-3√5
Simplify
3+√5 3-√5​

Answer 1

Step-by-step explanation:

(7+3√5 )(7-3√5)

(a+b)(a-b)

49-45

4

(3+√5)(3-√5)

9-5

4

Answer 2

$\frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} } \\ \\ = \frac{(7 + 3 \sqrt{5} )(3 - \sqrt{5}) - (7 - 3 \sqrt{5} )(3 + \sqrt{5} ) }{9 - 5} \\ \\ = \frac{21 - 7 \sqrt{5} + 9 \sqrt{5} - 15 - 21 - 7 \sqrt{5} + 9 \sqrt{5} + 15 }{4} \\ \\ = \frac{4 \sqrt{5} }{4} \\ \\ = \sqrt{5}$