Find the roots of the each of the following equations, if they exist, by applying the quadratic formula:

contexto.140

3 years ago

The given equation is

$\begin{array}{l} \frac{1}{x}-\frac{1}{x-2}=3, x \neq 0,2 \\ \Rightarrow \frac{x-2-x}{x(x-2)}=3 \\ \Rightarrow \frac{-2}{x^{2}-2 x}=3 \\ \Rightarrow-2=3 x^{2}-6 x \\ \Rightarrow 3 x^{2}-6 x+2=0 \end{array}$

This equation is of the form , where and .

Discriminant,

So, the given equation has real roots.

Now,

Hence, and are the roots of the given equation.