Question

If x + 1/x = √5 , find the values of x² + 1/x² and x - 1/x

Answer 1

hello users ......

given that
x + 1/x = √5

we have to find
x² + 1/x² and x - 1/x = ?

solution :-
we know that
x² + y² = (x+y)² - 2xy
and
also
x² + y² = (x-y)² +2xy

now ,
(x+1/x) = √5
=> (x² + 1/x² ) = (x+ 1/x)² -2 × x × 1/x

=> (x² + 1/x² ) = √5² -2
= 5 -2 = 3 answer

and
also
x² +1/x² = (x-1/x)² +2 ×x × 1/x
=> 3 = (x -1/x)² +2
=> 3-2 = (x-1/x)²
=> (x-1/x)² = 1

=> (x-1/x) = 1 answer

⭐⭐ hope it helps ⭐⭐