Question

what is the solution

Answer 1

Hey user

Here is your answer :-

$\frac{4 + \sqrt{2} }{2 + \sqrt{2} } \\ \\ = \frac{(4 + \sqrt{2})(2 - \sqrt{2}) }{(2 + \sqrt{2})(2 - \sqrt{2}) } \\ \\ = \frac{2(4 + \sqrt{2}) - \sqrt{2} (4 + \sqrt{2} )}{ {2}^{2} - { \sqrt{2} }^{2} } \\ \\ = \frac{8 + 2 \sqrt{2} - 4 \sqrt{2} - 2 }{4 - 2} \\ \\ = \frac{6 - 2 \sqrt{2} }{2} \\ \\ = \frac{2(3 - \sqrt{2} }{2} \\ \\ 3 - \sqrt{2} \\ \\ so \: p = 3 \: and \: q = - \sqrt{2}$

thank you.