Question: If L,M and N are the roots of the equation
$$x^3 -2x^2 +3x-1=0$$
Then , find
$$1) L+M+N$$
$$2)\frac{1}{L}+\frac{1}{M}+\frac{1}{N}$$
I know the relation between the roots of the cubic equation but i want to get it using this equation ?

Answer: 
So, you know that $LMN=1$, $LM+MN+NL=3$, $L+M+N=2$. (Vieta's formulas.) This answers the first question.

The second one: use the fact that $\frac{1}{L}+\frac{1}{M}+\frac{1}{N}=\frac{LM+MN+NL}{LMN}$.
**HINT**

$$L+M+N = 2$$

$$\frac{1}{L}+\frac{1}{M}+\frac{1}{N}=\frac{LM+MN+NL}{LMN}=3$$

**NOTE**

to find this relations **simply expand**

$$(x-L)(x-M)(x-N)=0$$