Đáp án+Giải thích các bước giải:
Đặt `A=-5x^2-4x+1`
`A=-5x^2-2.\sqrt{5}x.\frac{2\sqrt{5}}{5}-\frac{4}{5}+\frac{9}{5}`
`A=-(5x^2+2.\sqrt{5}x.\frac{2\sqrt{5}}{5}+\frac{4}{5})+\frac{9}{5}`
`A=-(\sqrt{5}x+\frac{2\sqrt{5}}{5})^2+\frac{9}{5}`
`(\sqrt{5}x+\frac{2\sqrt{5}}{5})^2≥0`
`⇔-(\sqrt{5}x+\frac{2\sqrt{5}}{5})^2≤0`
`⇔-(\sqrt{5}x+\frac{2\sqrt{5}}{5})^2+\frac{9}{5}≤\frac{9}{5}`
Dấu `"="` xảy ra khi
`-(\sqrt{5}x+\frac{2\sqrt{5}}{5})^2=0`
`⇔\sqrt{5}x+\frac{2\sqrt{5}}{5}=0`
`⇔\sqrt{5}x=\frac{-2\sqrt{5}}{5}`
`⇔x=\frac{-2}{5}`
Vậy `A_{min}=\frac{9}{5}⇔x=\frac{-2}{5}`
