\(A=-3x^2+6x-7=-3\left(x^2-2x+1-1\right)-7\)
\(=-3\left(x-1\right)^2-4\le-4\)Dấu ''='' xảy ra khi x = 1
\(B=-2x^2+5x+1=-2\left(x^2-\dfrac{5}{2}x\right)+1\)
\(=-2\left(x^2-2.\dfrac{5}{4}x+\dfrac{25}{16}-\dfrac{25}{16}\right)+1\)
\(=-2\left(x-\dfrac{5}{4}\right)^2+\dfrac{33}{8}\le\dfrac{33}{8}\)Dấu ''='' xảy ra khi x = 5/4
C;D chỉ có GTNN thôi bạn nhé \(C=2x^2-8x+13=2\left(x^2-4x+4-4\right)+13\)
\(=2\left(x-2\right)^2+5\ge5\)Dấu ''='' xảy ra khi x = 2
\(D=x^2-3x+5=x^2-2.\dfrac{3}{2}x+\dfrac{9}{4}-\dfrac{9}{4}+5\)
\(=\left(x-\dfrac{3}{2}\right)^2+\dfrac{11}{4}\ge\dfrac{11}{4}\)Dấu ''='' xảy ra khi x = 3/2
d: Ta có: \(D=x^2-3x+5\)
\(=x^2-2\cdot x\cdot\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{11}{4}\)
\(=\left(x-\dfrac{3}{2}\right)^2+\dfrac{11}{4}\ge\dfrac{11}{4}\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{3}{2}\)
\(B=-2x^2+5x+1\)
\(=-2\left(x^2-\dfrac{5}{2}x-\dfrac{1}{2}\right)\)
\(=-2\left(x^2-2\cdot x\cdot\dfrac{5}{4}+\dfrac{25}{16}-\dfrac{33}{16}\right)\)
\(=-2\left(x-\dfrac{5}{4}\right)^2+\dfrac{33}{8}\le\dfrac{33}{8}\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{5}{4}\)
