Question

x-1/x=3 ,x is not equal to zero,

Answer 1

Answer:

Required numeric value of x is either ( 3 + √13 ) / 2 or ( 3 - √13 ) / 2 or both.

Step-by-step explanation:

Given equation is x - 1 / x = 3

= > x - 1 / x = 3

= > ( x^2 - 1 ) / x = 3

= > x^2 - 1 = 3x

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

By using quadratic equation : According to which, if an equation is in the form of ax^2 + bx + c = 0, x of this equation is different from the x of the above equation, then

$x =\dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a}$

On comparing the above equation with ax^2 + bx + c = 0, we get

a = 1 , b = - 3 and c = - 1

Thus,

$\implies x = \dfrac{ - ( -3) \pm \sqrt{( - 3) {}^{2} - 4( - 1 \times 1) } }{2 \times 1} \\ \\ \\ \implies x = \dfrac{3 \pm \sqrt{9 + 4} }{2} \\ \\ \\ \implies x = \dfrac{3 \pm \sqrt{13} }{2}$

= > x = ( 3 + √13 ) / 2 or ( 3 - √13 ) / 2

Hence the required numeric value of x is either ( 3 + √13 ) / 2 or ( 3 - √13 ) / 2 or both.