Question

Dacă X1,X2 sunt rădăcinile ecuaţiei X patrat -X +1 = 0 si S=1/X1 + 1/X2
, atunci S=?

Answer 1

x²-x+1 = 0
a = 1
b = -1
c = 1
$s = \frac{1}{x_1} + \frac{1}{x_2} = \frac{x_1+x_2}{x_1 x_2} = \frac{S}{P}$
$S= x_1 + x_2 = -\frac{b}{a} = -\frac{-1}{1} = 1$
$P = x_1x_2 = \frac{c}{a} = \frac{1}{1} = 1$
⇒ $s = \frac{S}{P} = \frac{1}{1} = 1$