Question

If a=9-4√5,find a-1/a​

Answer 1

Answer:

hey there❤ur answer is in attachment hope u like it mark as brainlist.

Answer 2

$\sf given : - \: a = 9 - 4 \sqrt{5} \\ \\ \sf \therefore \: \frac{1}{a} = \frac{1}{9 - 4 \sqrt{5} } \\ \\ \sf rationalizing \\ \\ \sf = \frac{1}{9 - 4 \sqrt{5} } \times \frac{9 + 4 \sqrt{5} }{9 + 4 \sqrt{5} } \\ \\ \sf = \frac{9 + 4 \sqrt{5} }{(9 - 4 \sqrt{5} )(9 + 4 \sqrt{5}) } \\ \\ \sf = \frac{9 + 4 \sqrt{5} }{ {(9)}^{2} - ( {4 \sqrt{5}) }^{2} } \\ \\ \sf = \frac{9 + 4 \sqrt{5} }{81 - 80} \\ \\ \sf = 9 + 4 \sqrt{5} \\ \\ \sf hence \: value \: of \: a - \frac{1}{a} = 9 - 4 \sqrt{5} \\ - \sf (9 + 4 \sqrt{5} ) \\ \\ \sf = \cancel9 - 4 \sqrt{5} - \cancel9 - 4 \sqrt{5} \\ \\ \sf = \boxed{ - 8 \sqrt{5}}$