Question

Sejam x1 e x2 das raízes da equação 2x² - 3x - 5=0. Determine:a.) 1/x1 + 1/x2

Answer 1

$2x^2-3x-5=0$

Pela relação das raízes  temos :

$a=2\\b=-3\\c=-5\\\\\frac{-b}{a}=x1+x2\\\\\frac{3}{2}=x1+x2\\\\\frac{c}{a}=x1x2\\\\\frac{-5}{2}=x1x2\\\\\frac{1}{x1}+\frac{1}{x2}=\frac{x2+x1}{x1x2}\\\\=\frac{\frac{3}{2}}{\frac{-5}{2}}=\frac{3}{2}.\frac{2}{-5}=\boxed{\frac{-3}{5}}$