Question

Find the roots of the following equations x-1/x=3,x≠0 ​

Answer 1

Answer:

this is your answer..... hope it's useful for you

Answer 2

Answer:

$\large \bold{x = - \frac{1}{2} }$

or

$x=\frac{3}{2}+i\frac{\sqrt{5}}{2}$

$x=\frac{3}{2}-i\frac{\sqrt{5}}{2}$

Step-by-step explanation:

given

$\frac{x - 1}{x} = 3$

$= > x - 1 = 3x$

$= > 2x = - 1$

$= > x = - \frac{1}{2}$

or

$x-\frac{1}{x}=3$

$x^2-3x-1=0$

$x^2-3x+\frac{9}{4}=-\frac{5}{4}$

$(x-\frac{3}{2})^2=\frac{5}{4}i^2$

$x-\frac{3}{2}=\sqrt{\frac{5}{4}i^2}$

$x-\frac{3}{2}=|i\frac{\sqrt{5}}{2}|$

$x=\frac{3}{2}+i\frac{\sqrt{5}}{2}$

$x=\frac{3}{2}-i\frac{\sqrt{5}}{2}$

Hope it helps