Cum se rezolva problema aceasta:

Aratati ca [tex]x^2+x+1\ \textgreater \ 0[/tex] ,∀ x ∈ R.


Răspuns :

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Vezi imaginea 102533

[tex]\it x^2+x+1 = x^2+x+\dfrac{1}{4} +\dfrac{3}{4} =\left(x+\dfrac{1}{2}\right)^2 +\dfrac{3}{4} \geq\dfrac{3}{4} \ \textgreater \ 0[/tex]