Question

9. If x = 1/x-5 and x != 5, find : x2 – 1/x2​

Answer 1

Answer:

Given :

( x + 1 /x ) = 5

We need to find x2 + 1 / x2

( x + 1 / x )2 = 25

= x2 + 1 / x2 + 2 (x)(1/x) = 25

= x2 + 1/x2 + 2 = 25

= x2 + 1 / x2 = 25 – 2

= x2 + 1 / x2=23

Hence x2 + 1 / x2 = 23

Answer 2

Answer:-

$\frac{ x + 1 }{x {}^{2} }= 25 \\ \\ = x {}^{2}  + \frac{1}{ {x}^{2} }  + 2 (x) (\frac {1}{x} )= 25 \\ \\ = x {}^{2}  + \frac{1}{ {x}^{2} }  + 2 = 25 \\ \\ = {x}^{2} + \frac{1}{ {x}^{2} }  = 25 – 2 \\ \\ = {x}^{2} + \frac{1}{x {}^{2} } =23$