Question

Sa se calculeze 1/x1 +1/x2 știind ca x1 și x2 sunt soluțiile ecuației x^2-x-2=0

Answer 1

$\frac{1}{x1} + \frac{1}{x2} = \frac{x2+x1}{x1*x2}$
s=x1+x2=$\frac{-b}{a} =1$
x1+x2=1
P=x1*x2=$\frac{c}{a} =-2$
x1+x2=1
x1*x2=-2
$\frac{1}{x1} + \frac{1}{x2} = \frac{x2+x1}{x1*x2}$=$\frac{1}{-2} = \frac{-1}{2}$

Answer 2

$\displaystyle \frac{1}{x_1} + \frac{1}{x_2} ,~x^2-x-2=0 \\ \\ a=1,~b=-1,~c=-2 \\ \\ \frac{1}{x_1} + \frac{1}{x_2} = \frac{x_1+x_2}{x_1 \cdot x_2} = \frac{s}{p} \\ \\ s=x_1+x_2=- \frac{b}{a} =- \frac{-1}{1} =1 \\ \\ p=x_1 \cdot x_2= \frac{c}{a} = \frac{-2}{1} =-2 \\ \\ \frac{1}{x_1} + \frac{1}{x_2} = \frac{x_1+x_2}{x_1 \cdot x_2} = \frac{s}{p} = \frac{1}{-2} =- \frac{1}{2}$