Question

Daca x1 si x2 sunt radacinile ecuatiei $x^{2}$+5x-2=0, fara sa rezolvati ecuatia, calculati
$\frac{x_{2} }{x_{1} } +\frac{x_{1} }{x_2} }$

Answer 1

$\it \dfrac{x_2}{x_1}+\dfrac{x_1}{x_2}=\dfrac{x_2^2+x_1^2}{x_1x_2}=\dfrac{(x_1+x^2)^2-2x_1x_2}{x_1x_2}=\dfrac{(-5)^2-2\cdot2}{-2}=-10,5$