\(a,C=3x^2+4x+7\)
\(=3\left(x^2+\dfrac{4}{3}x+\dfrac{7}{3}\right)\)
\(=3\left(x^2+\dfrac{4}{3}x+\dfrac{4}{9}+\dfrac{17}{9}\right)\)
\(=3\left(x^2+\dfrac{4}{3}x+\dfrac{4}{9}\right)+\dfrac{17}{3}\)
\(=3\left(x+\dfrac{2}{3}\right)^2+\dfrac{17}{3}\)
Vì: \(3\left(x+\dfrac{2}{3}\right)^2\ge0\forall x\)
\(\Rightarrow3\left(x+\dfrac{2}{3}\right)^2+\dfrac{17}{3}\ge\dfrac{17}{3}>0\forall x\)
Hay: C > 0 với mọi x
\(b,D=2x^2-5x+5\)
\(=2\left(x^2-\dfrac{5}{2}x+\dfrac{5}{2}\right)\)
\(=2\left(x^2-\dfrac{5}{2}x+\dfrac{25}{16}+\dfrac{15}{16}\right)\)
\(=2\left(x^2-\dfrac{5}{2}x+\dfrac{25}{16}\right)+\dfrac{15}{8}\)
\(=2\left(x-\dfrac{5}{4}\right)^2+\dfrac{15}{8}\)
Vì: \(2\left(x-\dfrac{5}{4}\right)^2\ge0\forall x\)
\(\Rightarrow2\left(x-\dfrac{5}{4}\right)^2+\dfrac{15}{8}\ge\dfrac{15}{8}>0\forall x\)
Hay: D > 0 với mọi x
=.= hok tốt!!
