Question

a. x^2+2x+2
b. x^2-4x+6
c. 9x^2+24x+17
d. 17-8x+x
Aratati ce urmatoarele expresii sunt pozitive oricare ar fi nr. real x :

Answer 1

$x^{2}$+2x+2=$x^{2}$+2x+1+1=$(x+1)^{2}$+1>0
$x^{2}$-4x+6=$x^{2}$-4x+4+2=$(x-2)^{2}$+2>0
[tex] 9x^{2} +24x+17=9x^{2} +24x+16+1= (3x+4)^{2} +1\ \textgreater \ 0 [/tex]
La d este corect? Nu este nimic la puterea a doua?
17-8x+$x^{2}$=1+16-8x+$x^{2}$=1+$(4-x)^{2}$>0