a) \(x^4+2019x^2+2018x+2019\)
\(=\left(x^4-x\right)+\left(2019x^2+2019x+2019\right)\)
\(=x\left(x^3-1\right)+2019\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2019\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x\left(x-1\right)+2019\right]\)
\(=\left(x^2+x+1\right)\left(x^2-x+2019\right)\)
b) \(E=2x^2-8x+1=2x^2-8x+8-7\)
\(=2\left(x^2-4x+4\right)-7=2\left(x-2\right)^2-7\)
Vì \(2\left(x-2\right)^2\ge0\forall x\Rightarrow E\ge-7\)
Dấu "=" xảy ra <=> \(2\left(x-2\right)^2=0\Leftrightarrow x-2=0\Leftrightarrow x=2\)
Vậy MinE = -7 <=> x = 2
b) \(E=2x^2-8x+1\)
\(E=2\left(x^2-4x+\frac{1}{2}\right)\)
\(E=2\left(x^2-2\cdot x\cdot2+2^2+\frac{7}{2}\right)\)
\(E=2\left[\left(x-2\right)^2+\frac{7}{2}\right]\)
\(E=2\left(x-2\right)^2+7\ge7\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x-2=0\Leftrightarrow x=2\)
Vậy....
