Question

Sendo X' e X'' as raizes da equação X + 1 = 8 - x / X.
Entao o valor de ( X ') 2 + ( X'') 2 e igual a :::
A=12
B =8
C = - 8
D= - 2
E= 20

Obs:: Somente o 8 - X
que eh sobre X..

Obg a quem ajudar..

Answer 1

Olá Cintia
(x+1)=(8-x)/x
(x+1)/1=(8-x)/x
(x+1).x=1.(8-x)
x²+x=8-x
x²+x+x=8
x²+2x=8
x²+2x-8=0
(x'+x'')²=x'²+2.x'.x''+x''²
Soma=-b/a => -2/1 => -2
Produto=c/a => -8/1 = -8
(-2)²=x'²+2.(-8)+x''²
4=x'²-16+x''²
4+16=x'²+x''² 
20=x'²+x''²
x'²+x''²=20 #

Answer 2

$Resolu\c{c}\~ao \to \left\{\begin{array}{ccc} \frac{8-x}{x} = x+1 \\\\x*(x+1) = 8-x\\\\x^2+x = 8-x\\\\x^2 + x+x-8 = 0\\\\x^2+2x-8=0\\\\x' = 2\\x''=-4\end{array}\right\to \left\begin{array}{ccc}x^2+2x-8\\\\\Delta = 4-4*(1)*(-8) \\\Delta = 4+32 = 36\\\\x = \frac{-2\pm6}{2} \\\\\boxed{(2)^2+(-4)^2 = 4+16 = 20}\end{array}\right$

Letra E.

Espero ter ajudado. :))