Question

If (x+1/x)=12,then find the value of (x-1/x) .

Answer 1

Answer:

√140 or 2√35

Step-by-step explanation:

$x + \frac{1}{x} = 12$

Squaring on both sides we get,

${x}^{2} + { \frac{1}{x} }^{2} + 2 = 144$

${x}^{2} + { (\frac{1}{x}) }^{2} = 142$

Now, we know that

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

Put the value you get,

$x - \frac{1}{x} = \sqrt{140}$