Folosim formula [tex]a^2+2ab+b^2=(a+b)^2[/tex], unde a=x si b=1/2
[tex]x^2+x+1=x^2+2\cdot\dfrac12\cdot x+\dfrac14+1-\dfrac14=[/tex]( Am adunat 1/4 ca sa pot folosi formula, apoi l-am scazut oentru a nu se modifica enuntul.)
[tex]=\left(x+\dfrac12\right)^2+\dfrac34\geq\dfrac34>0,\forall x\in R[/tex]
