Question

Answer 1

a) \(9x^2-6x+3=\left(3x-1\right)^2+2\)

Vì \(\left(3x-1\right)^2\ge0\forall x\)

\(\Rightarrow9x^2-6x+3>0\)

b) \(3x-x^2-7=-\left(x^2-3x+7\right)=-\left(x-\dfrac{3}{2}\right)^2-\dfrac{19}{4}\)

Vì \(-\left(x-\dfrac{3}{2}\right)^2\le0\forall x\)

\(\Rightarrow3x-x^2-7< 0\)