`#kehuydiet`
a) $B=-4x^2+22x+15$
$B=-4x^2+22x-\dfrac{121}4+\dfrac{181}4$
$B=-(4x^2-22x+\dfrac{121}4)+\dfrac{181}4$
$B=-(2x-\dfrac{11}2)^2+136$
Vì $-(2x-\dfrac{11}2)^2\le 0\;\forall x\in \mathbb{R}$
$⇒ -(2x-\dfrac{11}2)^2+\dfrac{181}4\le \dfrac{181}4 \;\forall x\in \mathbb{R}$
Vậy $\max B=\dfrac{181}4$ khi $2x-\dfrac{11}2=0 ⇔ x=\dfrac{11}4$
b) $C=2x^2+y^2-2xy-2x+2017$
$C=(x^2-2xy+y^2)+(x^2-2x+1)+2016$
$C=(x-y)^2+(x-1)^2+2016$
Vì $(x-y)^2+(x-1)^2\ge 0\;\forall x\in \mathbb{R}$
$⇒ (x-y)^2+(x-1)^2+2016\ge 2016\;\forall x\in \mathbb{R}$
Vậy $\min C=2016$ khi $\begin{cases}x-y=0\\x-1=0\end{cases}⇔\begin{cases}x=1\\y=1\end{cases}$
