Answers

2016-03-25T14:53:38+05:30
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

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   



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

1/x = x+5  
 x - 1/x = -5
 </span> x^2 + 1/x^2 - 2(x)(1/x) = 25

 x^2 + 1/x^2 = 23

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