Question

find a square minus b square if a = 3 minus root 5 divided by 3 plus root 5 and b = 3 plus root 5 divided by 3 minus root 5

Answer 1

Answer:

0

Step-by-step explanation:

$a \: = 3 - \frac{ \sqrt{5} }{3} + \sqrt{5} \\ b = 3 + \frac{ \sqrt{5} }{3} - \sqrt{5} \\ {a}^{2} = {(3 - \frac{ \sqrt{5} }{3} + \sqrt{5}) }^{2} = 9 - \frac{5}{9} + 5 = 14 - \frac{5}{9} \\ {b}^{2} = {(3 + \frac{ \sqrt{5} }{3} - \sqrt{5} ) }^{2} = 9 + \frac{5}{9} + 5 = 14 + \frac{5}{9} \\ {a}^{2} - {b}^{2} = 14 - \frac{5}{9} - 14 + \frac{5}{9} \\ = 0$