Question

Dau 30 puncteee!
1) Se considera expresia E=$a^{2} + 2a+2$
a) Calculati valorile lui E daca a apartine {-1,0,1}
b) Aratati ca E>0, oricare ar fi a apartine R
c) Descompuneti in factori expresia E- 10

Answer 1

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Answer 2

a) $E(-1)= (-1)^{2} +2*(-1)+2=1-2+2=1$
$E(0)= 0^{2} +2*0+2=0+0+2=2$
$E(1)= 1^{2} +2*1+2=1+2+2=5$
b)$E= a^{2} +2a+2=(a^{2} +2a+1)+1$⇒
$E= (a+1)^{2} +1$
$\left \{ {{ (a+1)^{2} \geq 0, \ pentru \ a∈R } \atop {1>0}} \right.$⇒
$E>0, \ pentru \ a∈R$
c)$E-10= a^{2} +2a+2-10= a^{2} +2a-8= (a^{2} +2a+1)-9$⇒
$E-10= (a+1)^{2} - 3^{2} =(a+1-3)*(a+1+3)$⇒
$E-10=(a-2)*(a+4)$