a)\(A=5x^2-7x-4=5\left(x^2-\dfrac{7}{5}x-\dfrac{4}{5}\right)=5\left(x^2-\dfrac{7}{5}x+\dfrac{49}{100}-\dfrac{129}{100}\right)=5\left[\left(x-\dfrac{7}{10}\right)^2-\dfrac{129}{100}\right]\ge5.-\dfrac{129}{100}=-\dfrac{129}{20}\)Dấu = xảy ra <=> \(x=\dfrac{7}{10}\)
b)\(B=6x^2+5x+4=6\left(x^2+\dfrac{5}{6}x+\dfrac{2}{3}\right)=6\left(x^2+\dfrac{5}{6}x+\dfrac{25}{144}+\dfrac{71}{144}\right)=6\left[\left(x+\dfrac{5}{12}\right)^2+\dfrac{71}{144}\right]\ge\dfrac{71}{24}\)
Dấu = xảy ra <=> \(x=-\dfrac{5}{12}\)
c)\(C=2x^2+2x+2=2\left(x^2+x+1\right)=2\left(x^2+x+\dfrac{1}{4}+\dfrac{3}{4}\right)=2\left[\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}\right]\ge\dfrac{3}{2}\)
Dấu = xảy ra <=> \(x=-\dfrac{1}{2}\)
d)\(D=8x^2-8x+7=8\left(x^2-x+\dfrac{7}{8}\right)=8\left(x^2-x+\dfrac{1}{4}+\dfrac{5}{8}\right)=8\left[\left(x-\dfrac{1}{2}\right)^2+\dfrac{5}{8}\right]\ge5\)
Dấu = xảy ra <=> \(x=\dfrac{1}{2}\)
