Question

find the rational number p and q if

Answer 1

$rationalisation \\ (7 + \sqrt{5} )(7 + \sqrt{5} ) \div {7}^{2} - ( { \sqrt{5}) }^{2} - (7 - \sqrt{5} )(7 - \sqrt{5} ) \div {7}^{2} - { \sqrt{5} }^{2} = p - 7 \sqrt{5} q \\ \\ (49 + 5 + 14 \sqrt{5}) \div (49 - 5)- (49 - 5 + 14 \sqrt{5} ) \div (49 - 5) \: = p - 7 \sqrt{5} q \\ (14 \sqrt{5} + 14 \sqrt{5} ) \div 44 = p - 7 \sqrt{5} q \\ 2 8 \sqrt{5} \div 44 = p - 7 \sqrt{5} q \\0 + 4 \times 7 \sqrt{5} \div 44 = p - 7 \sqrt{5} q \\ p = 0 \\ q = -4 \div 44$

Answer 2

$\bold{Answer :}$

Now,

(7 + √5)/(7 - √5) - (7 - √5)/(7 + √5)

= {(7 + √5)(7 + √5) - (7 - √5)(7 - √5)}/{(7 - √5)(7 + √5)}

= (49 + 14√5 + 5 - 49 + 14√5 - 5)/(49 - 5)

= (28√5)/44

= (7√5)/11

Given that,

(7√5)/11 = p - 7√5 q

So, p = 0 and q = - 1/11

#$\bold{MarkAsBrainliest}$