Question

Aratati ca numarul A= x(x-1)(x-2)(x-3) +1 este un numar real nenegativ oricare ar fi x € R

Answer 1

[tex]A=x(x-1)(x-2)(x-3)+1\\ A=[x(x-3)]\cdot [(x-1)(x-2)]+1\\ A=(x^2-3x)(x^2-2x-x+2)+1\\ A=(x^2-3x)(x^2-3x+2)+1\\ Not. x^2-3x=t\\ A=t(t+2)+1\\ A=t^2+2t+1\\ A=(t+1)^2=(x^2-3x+1)^2\geq 0\ si\ \in \mathbb{R}[/tex]