Question

solve this question fast please if you know.
do in notebpok if possible.
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Answer 1

Answer:

$\frac{2 - \sqrt{5} }{2 + \sqrt{5} } = \frac{(2 - \sqrt{5})^{2} }{(2 + \sqrt{5})(2 - \sqrt{5}) } = 4 \sqrt{5} - 9$

$\frac{2 + \sqrt{5} }{2 - \sqrt{5} } = \frac{(2 + \sqrt{5} ) ^{2} }{(2 - \sqrt{5})(2 + \sqrt{5}) } = - 4 \sqrt{5} - 9$

After rationalising, you get

p= 4√5 - 9, q = -4√5 - 9

(i) p+q = (4√5 - 9) + (-4√5 - 9) = -18

(ii) p-q = (4√5 - 9) - (-4√5 - 9) = 8√5

(iii) p²+q² = (4√5 - 9)² + (-4√5 - 9)² = 322

(iv) p²-q² = (4√5 - 9)² - (-4√5 - 9)² = -72√5