P = (1-2x)(x-3) = -2x^2 + 7x - 3
bấm phím trên Mt casio 570VN-plus được kq: Pmin = 25/8 = 3.125
\(P=\left(1-2x\right)\left(x-3\right)\)
\(\Leftrightarrow P=x-3-2x^2+6x\)
\(\Leftrightarrow P=-2x^2+7x-3\)
\(\Leftrightarrow P=-2x^2+7x-\dfrac{49}{8}+\dfrac{25}{8}\)
\(\Leftrightarrow P=-2\left(x^2-\dfrac{7}{2}x+\dfrac{49}{16}\right)+\dfrac{25}{8}\)
\(\Leftrightarrow P=-2\left[x^2-2.x.\dfrac{7}{4}+\left(\dfrac{7}{4}\right)^2\right]+\dfrac{25}{8}\)
\(\Leftrightarrow P=-2\left(x-\dfrac{7}{4}\right)^2+\dfrac{25}{8}\)
Vậy GTLN của \(P=\dfrac{25}{8}\) khi \(x-\dfrac{7}{4}=0\Leftrightarrow x=\dfrac{7}{4}\)