Question

find a and b if 7+3root5/3+root5-7-3root5/3-root5= a+b root5

Answer 1

Hope this helps you ☺

Answer 2

$\frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} } = a + b \sqrt{5} \\ or. \: \frac{(7 + 3 \sqrt{5})(3 - \sqrt{5}) - (7 - 3 \sqrt{5} )(3 + \sqrt{5} ) }{(3 + \sqrt{5})(3 - \sqrt{5} )} = a + b \sqrt{5} \\ or. \: \frac{(21 - 7 \sqrt{5} + 9 \sqrt{5} - 15) - (21 - 9 \sqrt{5} + 7 \sqrt{5} - 15) }{ {3}^{2} - {( \sqrt{5} )}^{2} } = a + b \sqrt{5} \\ or. \: \frac{6 + 2 \sqrt{5} - 6 + 2 \sqrt{5} }{9 - 5} = a + b \sqrt{5} \\ or. \: \frac{4 \sqrt{5} }{4} = a + b \sqrt{5} \\ or. \: \sqrt{5} = a + b \sqrt{5} \\ \\ so \: a = 0....and \: \: b = 1$
Hope this is ur required answer
Proud to help you