Question

Să se calculeze 1/x1 +1/x2 , stiind ca x1 si x2 sunt solutiile ecuatiei x^2-x-2=0

Answer 1

x²-x--2=0
⇒ x₁+x₂=1
si x₁x₂=-2

1/x₁+1/x₂= (x₁+x₂)/x₁x₂= 1/-2= -1/2

O seara buna!

Answer 2

$\displaystyle x^2-x-2=0 \\ a=1,~b=-1,~c=-2 \\ s=x_1+x_2=- \frac{b}{a} =- \frac{-1}{1} =1 \\ p=x_1x_1= \frac{c}{a} = \frac{-2}{1} =-2 \\ \frac{1}{x_1} + \frac{1}{x_2} = \frac{x_1+x_2}{x_1x_2} = \frac{1}{-2} =- \frac{1}{2}$