Question

solve 7 + root 5 / 7-root 5 - 7 - root 5 / 7 + root 5 ​

Answer 1

Question:-

Solve:

$\frac{(7 + \sqrt{5}) }{(7 - \sqrt{5} )} - \frac{(7 - \sqrt{5}) }{(7 + \sqrt{5}) }$

Solution:-

LCM will be

$(7 - \sqrt{5} )(7 + \sqrt{5} )$

$49 - 5 = 44$

$\frac{(7 + \sqrt{5})(7 + \sqrt{5}) - (7 - \sqrt{5})(7 - \sqrt{5} ) }{44}$

$= \frac{ {(7 + \sqrt{5} )}^{2} - {(7 - \sqrt{5}) }^{2} }{44}$

=$\frac{(( {7})^{2} + { (\sqrt{5} })^{2} + 2 \times 7 \times \sqrt{5}) - (( {7})^{2} + ( \sqrt{5} )^{2} - 2 \times 7 \times \sqrt{5}) }{44}$

=$\frac{14 \sqrt{5} + 14 \sqrt{5} }{44}$

=$\frac{28 \sqrt{5} }{44}$

=$\frac{7 \sqrt{5} }{11}$