a) \(A=x^2+x+1\)
\(A=x^2+2\cdot x\cdot\frac{1}{2}+\frac{1}{4}+\frac{3}{4}\)
\(A=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x+\frac{1}{2}=0\Leftrightarrow x=\frac{-1}{2}\)
c) \(C=x^2\left(2-x^2\right)\)
\(C=2x^2-x^4\)
\(C=-\left(x^4-2x^2\right)\)
\(C=-\left[\left(x^2\right)^2-2\cdot x^2\cdot1+1^2-1\right]\)
\(C=-\left[\left(x^2-1\right)^2-1\right]\)
\(C=1-\left(x^2-1\right)^2\le1\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x^2-1=0\Leftrightarrow x=\left\{\pm1\right\}\)
b) \(B=5-8x-x^2\)
\(B=-\left(x^2+8x-5\right)\)
\(B=-\left(x^2+2\cdot x\cdot4+16-21\right)\)
\(B=-\left[\left(x+4\right)^2-21\right]\)
\(B=21-\left(x+4\right)^2\le21\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x+4=0\Leftrightarrow x=-4\)
