Question

10. If a = 9 - 4√5, find the value of (a – 1/a )^2


​

Answer 1

Step-by-step explanation:

a = 9 - 4√5

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

= {(9 - 4√5) - (9 + 4√5)}²

= (9 - 4√5 - 9 - 4√5)²

= (- 8√5)²

= 320

Hope it helps you........

please mark my answer as brainleist.........