Question

if X+1/X=3 than find the value of x-1/x​

Answer 1

Answer:

Given,

x + $\frac{1}{x}$ = 3

$(x + \frac{1}{x} )^{2}$ = $x^{2} + \frac{1}{x^{2} }$ + 2

or, 9 = $x^{2} + \frac{1}{x^{2} }$ + 2     Putting x + $\frac{1}{x}$ = 3

or,  $x^{2} + \frac{1}{x^{2} }$ = 7

Also,

$(x - \frac{1}{x})^{2}$ =  $x^{2} + \frac{1}{x^{2} }$ - 2

or, $(x - \frac{1}{x})^{2}$  = 7 - 2 =5   After putting  ($x^{2} + \frac{1}{x^{2} }$ = 7)

or, $(x - \frac{1}{x} )$ = $\sqrt{5}$