Đáp án+Giải thích các bước giải:
`A=36x^2-12x+10`
`A=36x^2-12x+1+9`
`A=(6x-1)^2+9`
`(6x-1)^2≥0∀x`
`⇔(6x-1)^2+9≥9`
Dấu `"="` xảy ra khi
`6x-1=0`
`⇔6x=1`
`⇔x=\frac{1}{6}`
Vậy `A_{min}=9⇔x=\frac{1}{6}`
------------------------------
`B=-x^2+7x+5`
`B=-x^2+2.x.\frac{7}{2}-\frac{49}{4}+\frac{69}{4}`
`B=-(x^2-2.x.\frac{7}{2}+\frac{49}{4})+\frac{69}{4}`
`B=-(x-\frac{7}{2})^2+\frac{69}{4}`
`(x-\frac{7}{2})^2≥0`
`⇔-(x-\frac{7}{2})^2≤0`
`⇔-(x-\frac{7}{2})^2+\frac{69}{4}≤\frac{69}{4}`
Dấu `"="` xảy ra khi
`x-\frac{7}{2}=0`
`⇔x=\frac{7}{2}`
Vậy `B_{max}=\frac{69}{4}⇔x=\frac{7}{2}`
