`A=x^2-9x-1`
`=x^2-2.x.\frac{9}{2}+(\frac{9}{2})^2-(\frac{9}{2})^2-1`
`=(x-\frac{9}{2})^2-\frac{85}{4}`
Vì `(x-\frac{9}{2})^2≥0∀x`
`⇒(x-\frac{9}{2})^2-\frac{85}{4}≥-\frac{85}{4}`
Vậy `A_min=-\frac{85}{4}⇔(x-\frac{9}{2})^2=0⇔x=\frac{9}{2}`
`B=3x^2+5x+3`
`=3(x^2+\frac{5}{3}x+1)`
`=3[x^2+2.x.\frac{5}{6}+(\frac{5}{6})^2-(\frac{5}{6})^2+1]`
`=3[(x+\frac{5}{6})^2\frac{11}{36}]`
`=3(x+\frac{5}{6})^2-\frac{11}{12}`
Vì `3(x+\frac{5}{6})^2≥0∀x`
`⇒3(x+\frac{5}{6})^2-\frac{11}{12}≥ -\frac{11}{12}∀x`
Vậy `B_min=-\frac{11}{12}⇔3(x+\frac{5}{6})^2=0⇔x=-\frac{5}{6}`
`D=7-4x^2-2x`
`=-4x^2-2x+7`
`=-4(x^2+\frac{1}{2}x-\frac{7}{4})`
`=-4[x^2+2.x.\frac{1}{4}+(\frac{1}{4})^2-(\frac{1}{4})^2-\frac{7}{4}]`
`=-4[(x+\frac{1}{4})^2-\frac{29}{16}]`
`=-4(x+\frac{1}{4})^2+\frac{29}{4}`
Vì `-4(x+\frac{1}{4})^2≤0∀x`
`⇒-4(x+\frac{1}{4})^2+\frac{29}{4}≤\frac{29}{4}∀x`
Vậy `D_max=\frac{29}{4}⇔x=-\frac{1}{4}`
