Question

if x^2+1/x^2=27 find x-1/x

Answer 1

$\textbf{ Hello Mate! }$

x² + 1 / x² = 27

( a - b )² = a² + b² - 2ab

( x - 1 / x )² = x² + 1 / x² - 2 × x × 1 / x

( x - 1 / x )² = 27 - 2

x - 1 / x = √25 or 5

$\boxed{Answer: \: = 5 }$

Hope it helps

Answer 2

Let the value of x - 1/x be 'a'

Lets rearrange the term x - 1/x

x - 1/x=a

Squaring both sides, we get :

x² + 1/x² - 2=a²

And since the value of x² + 1/x² = 27 (Given)

Putting the value in eq1 , we get :

27 - 2= a²

25 = a²

+-5 = a , where a = x - 1/x

So, x - 1/x = +-5

:)