Question

the roots of the equation 1/x - 1/x-2 =3 are A) 3+√5/2 B) 3+√3/3 C)3+√5/3 D)3+√3/2​

Answer 1

Answer:

a

Step-by-step explanation:

2x-2=3x^2-2x

putting values on equations

=3+under root 3/3

Answer 2

Answer:

1+1/√3

Step-by-step explanation:

$\frac{1}{x} - \frac{1}{x - 2} = 3$

$\frac{x - 2 - x}{ {x}^{2} - 2x } = 3$

$- 2 = 3 {x}^{2} - 6x$

$3 {x}^{2} - 6x + 2 = 0$

By using the method of square completion,

${x}^{2} - 2x + \frac{2}{3} = 0$

${x}^{2} - 2x = \frac{ - 2}{3}$

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

${x}^{2} - 2(1)(x) = \frac{ - 2}{3}$

${x}^{2} - 2x + 1 = \frac{ - 2}{3} + 1$

${(x - 1)}^{2} = \frac{1}{3}$

$x - 1 = ± \frac{1}{ \sqrt{3} }$

$x = 1 + \frac{1}{ \sqrt{3} } ;x = 1 - \frac{1}{ \sqrt{3} }$