Question

Find the value of p and q if 7-√3/7+√3+7+√3/7-√3=p-q√3

Answer 1

It's the answer of your question

Answer 2

$\frac{7 - \sqrt{3} }{7 + \sqrt{3} } + \frac{7 + \sqrt{3} }{7 - \sqrt{3} } = p - q \sqrt{3}$
rationalising the denominator or take LCM
$\frac{(7 - \sqrt{3})(7 - \sqrt{3}) + (7 + \sqrt{3})(7 + \sqrt{3} ) }{(7 - \sqrt{3} )(7 + \sqrt{3}) }$
$\frac{ {(7 - \sqrt{3}) }^{2} + {(7 + \sqrt{3}) }^{2} }{ {7}^{2} - { (\sqrt{3} })^{2} }$
open the identity
$\frac{49 + 3 - 14 \sqrt{3} + 49 + 3 + 14 \sqrt{3} }{49 - 3}$
$\frac{52 + 52}{46} = \frac{104}{46}$
so
$\frac{52}{23}$
= p-q√3
so value of p= 52/23
q=0