a ) \(9x^2-6x+12\)
\(=\left(3x\right)^2-2.3x+1+11\)
\(=\left(3x-1\right)^2+11\ge11>0\forall x\)
\(\Rightarrowđpcm\)
b ) \(2x^2-2x+8\)
\(=2\left(x^2-x+4\right)\)
\(=2\left(x^2-x+\dfrac{1}{4}+\dfrac{15}{4}\right)\)
\(=2\left[\left(x-\dfrac{1}{2}\right)^2+\dfrac{15}{4}\right]\)
\(=2\left(x-\dfrac{1}{2}\right)^2+\dfrac{15}{2}\ge\dfrac{15}{2}>0\forall x\)
\(\Rightarrowđpcm\)