Question

Subiectul 2,exercitiul 2 , punctele b),c). Va roooogggg

Answer 1

2. 
b) 
f = $(X+1)( X^{2}-X+1) + 2X(X+1)$
f = $(X+1)( X^{2} +X+1)$

c) Ne folosim de relatiile lui Viete.
$x_{1} + x_{2} + x_{3} = \frac{-b}{a} = -2$
$x_{1} x_{2} + x_{2} x_{3} + x_{1} x_{3} = \frac{c}{a} = a$
$x_{1} x_{2} x_{3} = \frac{-d}{a} = -b$

$x_{1} ( x_{1} -1)+ x_{2} ( x_{2} -1) + x_{3} ( x_{3} -1) = -2$
$x_{1} ^{2} - x_{1} + x_{2} ^{2} - x_{2} + x_{3} ^{2} - x_{3} = -2$
$x_{1} ^{2} + x_{2} ^{2}+x_{3} ^{2} - ( x_{1}+ x_{2}+x_{3}) = -2$
$x_{1} ^{2} + x_{2} ^{2}+x_{3} ^{2} = 4-2a$ ( obtinem aceasta relatie ridicand prima relatie a lui Viete la patrat).
$x_{1}+ x_{2}+x_{3} = -2$
⇒ $4-2a-(-2)=-2$
⇒ $6-2a=-2$ ⇒ $a=4$