a: \(3x^2-5x+7\)
\(=3\left(x^2-\dfrac{5}{3}x+\dfrac{7}{3}\right)\)
\(=3\left(x^2-2\cdot x\cdot\dfrac{5}{6}+\dfrac{25}{36}+\dfrac{59}{36}\right)\)
\(=3\left(x-\dfrac{5}{6}\right)^2+\dfrac{59}{12}\ge\dfrac{59}{12}\)
Dấu '=' xảy ra khi x=5/6
c: \(\left(x-3\right)^2+\left(x-2\right)^2\)
\(=x^2-6x+9+x^2-4x+4\)
\(=2x^2-10x+13\)
\(=2\left(x^2-5x+\dfrac{13}{2}\right)\)
\(=2\left(x^2-2\cdot x\cdot\dfrac{5}{2}+\dfrac{25}{4}+\dfrac{1}{4}\right)\)
\(=2\left(x-\dfrac{5}{2}\right)^2+\dfrac{1}{2}\ge\dfrac{1}{2}\)
Dấu '=' xảy ra khi x=5/2
d: \(\left(x-1\right)\left(x+3\right)+11\)
\(=x^2+2x-3+11\)
\(=x^2+2x+8=\left(x+1\right)^2+7\ge7\)
Dấu '=' xảy ra khi x=-1
