Question

If a = 9-4√5 then find the value of a=

-1\a​

Answer 1

Answer:

$a - \frac{1}{a} = - 8 \sqrt{5} .$

Step-by-step explanation:

$a = 9 - 4 \sqrt{5} \\ \\ \frac{1}{a} = \frac{1}{9 - 4 \sqrt{5} } \times \frac{(9 + 4 \sqrt{5} )}{(9 + 4 \sqrt{5}) } \\ \\ = \frac{9 + 4 \sqrt{5} }{81 - 80} \\ \\ = 9 + 4 \sqrt{5} \\ \\ therefore \: \: \: a - \frac{1}{a} = (9 - 4 \sqrt{5} ) - (9 + 4 \sqrt{5} ) \\ \\ = - 8 \sqrt{5} .$

Answer 2

Answer:

The answer is $-9-4\sqrt{5}$

Step-by-step explanation:

$\frac{-1}{a} = \frac{-1}{9-4\sqrt{5} }(\frac{9+4\sqrt{5} }{9+4\sqrt{5} })=\frac{-9-4\sqrt{5} }{9^{2}-(4\sqrt{5}) ^{2} } =\frac{-9-4\sqrt{5} }{81-16(5)} =\frac{-9-4\sqrt{5} }{81-80} = \frac{-9-4\sqrt{5} }{1}=-9-4\sqrt{5}$

I Hope this helps you...