Question

Considere X1 e X2 as raízes da equação x²-11x+28=0 e determine as expressões abaixo:

a) 1/x1 + 1/X2
b) x1² + x2²

Answer 1

Vamos lá:

$x^2 - 11x + 28 = 0 \\\ \Delta = (- 11)^2 - 4.1.28 \\\ \Delta = 121 - 112 \\\ \Delta = 9 \\\\ x_1 = \frac{- (- 11) + \sqrt{9}}{2.1} \\\ x_1 = \frac{11 + 3}{2} \\\ x_1 = \frac{14}{2} \\\ x_1 = 7 \\\ x_2 = \frac{- (- 11) - \sqrt{9}}{2.1} \\\ x_2 = \frac{11 - 3}{2} \\\ x_2 = \frac{8}{2} \\\ x_2 = 4$

Portanto:

a)
$\frac{1}{x_1} + \frac{1}{x_2} = \frac{1}{7} + \frac{1}{4} = \frac{11}{28}$
b)
${x_1}^2 + {x_2}^2 = 7^2 + 4^2 = 49 + 16 = 65$

Espero tet ajudado.