Question

determine rational number p and q if : 7+√5/7-√5-7-√5/7+√5=p-7√5q​

Answer 1

$\frac{7 + \sqrt{5} }{7 - \sqrt{5} } × \frac{7 + \sqrt{5} }{7 + \sqrt{5} } - \frac{7 - \sqrt{5}}{7 + \sqrt{5}} × \frac{7-\sqrt{5} }{7-\sqrt{5} } \\\\\frac{49+25+14\sqrt{5} }{44} - \frac{(49+25-14\sqrt{5} )}{44}$

$\frac{14\sqrt{5}+14\sqrt{5} }{44} = \frac{2 × 14\sqrt{5} }{44} = \frac{7\sqrt{15} }{11} \\\\ p-7\sqrt{5}q = \frac{7\sqrt{5} }{11} \\p=0 , q= \frac{-1}{11}$