Question

Solve the following equation:
(1/x)-(1/x-2)=3,x not equal to 0,2

Answer 1

Answer:

Required values of x are ( 3 ± √3 ) / 3.

Step-by-step explanation:

$\implies \dfrac{1}{x} - \dfrac{1}{x- 2} =3 \\ \\ \\ \implies \dfrac{ x - 2 - x}{x(x - 2)} = 3$

= > - 2 = 3( x )( x - 2 )

= > - 2 = 3[ x^2 - 2x ]

= > - 2 = 3x^2 - 6x

= > 3x^2 - 6x + 2 = 0

= > ( √3 x ) ^2 - 2( √3 × √3 )x + 2 = 0

= > ( √3 x )^2 - 2( √3x × √3 ) + 3 + 2 - 3 = 0 { Adding & subtracting 3 }

= > ( √3 x )^2 - 2( √3x × √3 ) + ( √3 )^2 - 1 = 0

= > ( √3 x - √3 )^2 - 1 = 0 { Using a^2 + b^2 - 2ab = ( a - b )^2 }

= > ( √3 x - √3 )^2 = 1

= > √3 x - √3 = ± 1

= > √3 x = √3 ± 1

= > x = ( √3 ± 1 ) / √3

= > x = ( 3 ± √3 ) / 3

Hence the required values of x are ( 3 ± √3 ) / 3.