a) Ta có: \(A=x^2+3x+3\)
\(=x^2+2\cdot x\cdot\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{3}{4}\)
\(=\left(x+\dfrac{3}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\forall x\)
Dấu '=' xảy ra khi \(x=-\dfrac{3}{2}\)
b) Ta có: \(B=x^2+4x+9\)
\(=x^2+4x+4+5\)
\(=\left(x+2\right)^2+5\ge5\forall x\)
Dấu '=' xảy ra khi x=-2
c) Ta có: \(C=-x^2+x+1\)
\(=-\left(x^2-x-1\right)\)
\(=-\left(x^2-2\cdot x\cdot\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{5}{4}\right)\)
\(=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{5}{4}\le\dfrac{5}{4}\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{1}{2}\)
d)Ta có: \(D=-4x^2+4x+1\)
\(=-\left(4x^2-4x-1\right)\)
\(=-\left(4x^2-4x+1-2\right)\)
\(=-\left(2x-1\right)^2+2\le2\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{1}{2}\)
e) Ta có: \(E=\dfrac{1}{16}x^2-9x+10\)
\(=\left(\dfrac{1}{4}x\right)^2-2\cdot\dfrac{1}{4}x\cdot18+324-314\)
\(=\left(\dfrac{1}{4}x-18\right)^2-314\ge-314\forall x\)
Dấu '=' xảy ra khi \(\dfrac{1}{4}x-18=0\)
hay x=72
f) Ta có: \(F=4x^4+12x^2+11\)
\(\Leftrightarrow F\ge11\forall x\)
Dấu '=' xảy ra khi x=0
