Question

simplify it plz urgent

Answer 1

Hey !! ⬅

x = a - 4√5

1/x = 1/a-4√5

rationalise it

1/x = a+4√5 /(a-4√5)(a+4√5)

=> a + 4√5/a² -( 4√5)²

=> a + 4√5/a²-80

hence x + 1/x

= a - 4√5 + a + 4√5/a²-80

=> a (a² - 80) - 4√5(a²-80) /a²-80

=> a³-80a - 4√5a²+320√5 /a²-80

=> a³ -80a 4√5a²+325√5 /a² -80 Answer

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hope it helps you !!!

@Rajukumar111

Answer 2

According to given sum,

$x = 9 - 4 \sqrt{5}$

given that,

$= > \: x + \frac{1}{x}$

By taking LCM,

$= > \: \frac{ {x}^{2} + 1 }{x}$
$= > \: \frac{( {9 - 4 \sqrt{5} )}^{2} + 1}{9 - 4 \sqrt{5} }$

$= > \: \frac{81 + 80 - 72 \sqrt{5 } + 1}{9 - 4 \sqrt{5} }$

$= > \: \frac{162 - 72 \sqrt{5} }{9 - 4 \sqrt{5} }$

$= > \: \frac{18(9 - 4 \sqrt{5}) }{9 - 4 \sqrt{5} }$

$= > \: 18$

Hence, ans is 18.

:-)Hope it helps u.