Question

if x+1/x=8, find x-1/x​

Answer 1

Answer:

±2√15

Step-by-step explanation:

Given that,

$x + \dfrac{1}{x} = 8$

To find the value of x -1/x

Squaring both the sides, we get,

$= > {(x + \frac{1}{x} )}^{2} = {8}^{2} \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 64 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 64 - 2 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 62$

Now, we know that,

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

Therefore, we will get,

$= > {(x - \frac{1}{x} ) }^{2} = 62 - 2 \\ \\ = > {(x - \frac{1}{x}) }^{2} = 60 \\ \\ = > x - \frac{1}{x} = \pm \sqrt{60} \\ \\ = > x - \frac{1}{x} = \pm2 \sqrt{15}$

Hence, the required value of (x-1/x) = ±2√15.