Question

if 3 + root 5 / 2 root 5 + 3 equal to a + b root 5 find the values of A and B easy answer equal to 1 by 11 and b is equal to 3 / 11

Answer 1

Hello Mate!

$\frac{3 + \sqrt{5} }{2 \sqrt{5} + 3 } = a + b \sqrt{5} \\ \frac{3 + \sqrt{5} }{2 \sqrt{5} + 3} \times \frac{ 2\sqrt{5} - 3 }{2 \sqrt{5} - 3} \\ = \frac{(3 + \sqrt{5} )(2 \sqrt{5} - 3) }{20 - 9} \\ = \frac{6 \sqrt{5 } - 9 + 2 \times 5 - 3 \sqrt{5} }{11} \\ = \frac{ 1 + \sqrt{5}(6 - 3) }{11} \\ = \frac{1 + 3 \sqrt{5} }{11} = a + b \sqrt{5} \\ a = \frac{1}{11} \: and \: b = \frac{3}{11}$

Hope its helps☺!