a: \(A=3\left(x^2-3x+\dfrac{5}{3}\right)\)
\(=3\left(x^2-2\cdot x\cdot\dfrac{3}{2}+\dfrac{9}{4}-\dfrac{7}{12}\right)\)
\(=3\left(x-\dfrac{3}{2}\right)^2-\dfrac{7}{4}\ge-\dfrac{7}{4}\)
Dấu '=' xảy ra khi x=3/2
b: \(B=\left(x-1\right)\left(3x+4\right)\)
\(=3x^2+4x-3x-4\)
\(=3x^2+x-4\)
\(=3\left(x^2+\dfrac{1}{3}x-\dfrac{4}{3}\right)\)
\(=3\left(x^2+2\cdot x\cdot\dfrac{1}{6}+\dfrac{1}{36}-\dfrac{49}{36}\right)\)
\(=3\left(x+\dfrac{1}{6}\right)^2-\dfrac{49}{12}\ge-\dfrac{49}{12}\)
Dấu '=' xảy ra khi x=-1/6
c: \(C=-\left(x^2+x+y^2-y-1\right)\)
\(=-\left(x^2+x+\dfrac{1}{4}+y^2-y+\dfrac{1}{4}-\dfrac{3}{2}\right)\)
\(=-\left(x+\dfrac{1}{2}\right)^2-\left(y-\dfrac{1}{2}\right)^2+\dfrac{3}{2}\le\dfrac{3}{2}\)
Dấu '=' xảy ra khi x=-1/2 và y=1/2