Question

if a=9-4√5 find the value of (a-1/a)^2​

Answer 1

$\: \bold \red{ || \: || \: your \: answer \: || \: || }$

$given \: \: \: \\ \bold \green{a = 9 - 4 \sqrt{5} } \\now \\ \\ to \: find \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red{ { = (a - \frac{1}{a}) }^{2} } \\ \\ therefore \\ \frac{1}{a} = \frac{1}{9 - 4 \sqrt{5} } \times \frac{9 + 4 \sqrt{5} }{9 + 4 \sqrt{5} } \: \: \: \bold \purple{.(rationalised)} \\ \\ \frac{1}{a} = \frac{9 + 4 \sqrt{5} }{81 - 80} \\ \frac{1}{a} = \frac{9 + 4 \sqrt{5} }{1} \\ \\ now \: according \: to \: question \\ \\ (a - \frac{1}{a} {)}^{2} = \\ \\ \: \: \: \: \: \: \: \bold \green{ = {(9 - 4 \sqrt{5} - 9 - 4 \sqrt{5} })^{2} } \\ \: \: \: \: \: \: \boxed {80} \: \bold \red {ans}$

$\: \bold \green{ \: till \: then \: be \: happy........}$