Question

If x=1/x-5 and x is not equal to 5 then find x^2-1/x^2

Answer 1

Hello and greetings

$x= \frac{1}{x - 5} ,$

x ≠ 5
Find $x^2 - 1/x^2$

Cross multiply in the given equation

$x= \frac{1}{x - 5} ,$

$(x)(x-5) = 1$

[tex]x^2 - 5x =1 x^2 - 5x + (5/2)^2 = 1 + (5/2)^2 (x- 5/2)^2 = 1 + (5/2)^2 Solve the above equation further and you get [/tex]

$x =\frac{5 + \sqrt{29}}{2} or \frac{5 - \sqrt{29}}{2}$

Now you can plug in these values and get your answer as 23
Plug in both values and you will get the same answer



Another approach(simpler approach

[tex]1/x = x+5 x - 1/x = -5[/tex]
 $</span> x^2 + 1/x^2 - 2(x)(1/x) = 25$

$x^2 + 1/x^2 = 23$