Question

Find the roots of equation, if they exist, by applying the quadratic formula:

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

, x # 0, 2

Answer 1

Given Equation is (1/x) - (1/x - 2) = 3.

It can be written as,

⇒ x - 2 - x = 3x(x - 2)

⇒ -2 = 3x(x - 2)

⇒ -2 = 3x^2 - 6x

⇒ 3x^2 - 6x + 2 = 0

∴ Comparing with ax^2 + bx + c = 0, a = 3, b = -6, c = 2.

D = b^2 - 4ac

   = (-6)^2 - 4(3)(2)

   = 36 - 24

   = 12.

Now, The solutions are:

(i)

$=>\frac{-b +\sqrt{D}}{2a}$

$=>\frac{-(-6)+\sqrt{12}}{6}$

$=>\frac{6 + \sqrt{12}}{6}$

$=>\frac{2(3+\sqrt{3})}{6}$

$=>\frac{3+\sqrt{3}}{3}$

(ii)

$=>\frac{-b-\sqrt{D}}{2a}$

$=>\frac{-(-6)-\sqrt{12}}{6}$

$=>\frac{6-\sqrt{12}} {6}$

$=>\frac{2(3-\sqrt{3})}{6}$

$=> \frac{3- \sqrt{3}}{3}$

Therefore, the roots of equation are:

$=>x=\boxed{\frac{3+ \sqrt{3}}{3}, \frac{3-\sqrt{3}}{3}}$

Hope it helps!

Answer 2

HERE IS YOUR ANSWER

HOPE IT HELPS YOU.