\(\left(x-3\right)\left(4x+5\right)+2019\)
\(=4x^2-7x-15+2019\)
\(=4x^2-7x+2004\)
\(=4\left(x^2-\frac{7}{4}x+501\right)\)
\(=4\left(x^2-\frac{7}{4}x+\frac{49}{64}+\frac{32015}{64}\right)\)
\(=4\left[\left(x-\frac{7}{8}\right)^2+\frac{32015}{64}\right]\)
\(=4\left[\left(x-\frac{7}{8}\right)^2\right]+\frac{32015}{16}\ge\frac{32015}{16}\)
Vậy GTNN của bt là \(\frac{32015}{16}\Leftrightarrow x-\frac{7}{8}=0\Leftrightarrow x=\frac{7}{8}\)
mk tưởng 7/4
