Question

if x+1/x=5 then x-1/x=?

Answer 1

Hi ,

x + 1/x = 5 ----( 1 )

( x - 1/x )² = ( x + 1/x )² - 4

= 5² - 4

= 25 - 4

= 21

x - 1/x = ±√21

I hope this helps you.

: )

Answer 2

Method (1):

Given Equation is x + 1/x = 5.

On Squaring both sides, we get

(x + 1/x)^2 = (5)^2

x^2 + 1/x^2 + 2 * x * 1/x = 25

x^2 + 1/x^2 + 2 = 25

x^2 + 1/x^2 = 25 - 2

x^2 + 1/x^2 = 23  ----------- (1)


Now,

(x - 1/x)^2 = x^2 + 1/x^2 - 2

                = 23 - 2

                = 21.


$x - \frac{1}{x} = \sqrt{21}$



Method (2):

We know that (a - b)^2 = (a + b)^2 - 4ab

Now,

(x - 1/x)^2 = (x + 1/x)^2 - 4 * x * 1/x

                = (5)^2 - 4

                = 25 - 4

                = 21.


$x - \frac{1}{x} = \sqrt{21}$


Hope this helps!