Question

x^2-3x+6 sa se calculeze valoarea expresiei E=1/x1+1/x2-x1-x2

Answer 1

Răspuns:

Explicație pas cu pas:

$\texttt{Se folosesc relatiile lui Viete}.\\S=x_1+x_2=\dfrac{-b}{a}=3\\\\P=x_1\cdot x_2=\dfrac{c}{a}=6\\E=\dfrac{1}{x_1}+\dfrac{1}{x_2}-x_1-x_2\\\\E=\dfrac{x_1+x_2}{x_1\cdot x_2}-(x_1+x_2)\\\\E=\dfrac{S}{P}-S\\\\E=\dfrac{3}{6}-3=\dfrac{1}{2}-3=-\dfrac{5}{2}$