Câu hỏi của Aki

Question

Tìm GTNN :

C = 4x² + 10y² - 4x + 10y - 2

Giúp mk vs ạ, mk cần gấp!!!

Kiệt Nguyễn · Accepted Answer

$C=4x^2+10y-4x+10y-2$

$=\left(4x^2-4x+1\right)+\left(10y^2+10y+\frac{5}{2}\right)-\frac{11}{2}$

$=\left(2x-1\right)^2+\left(\sqrt{10y}+\sqrt{\frac{5}{2}}\right)^2-\frac{11}{2}\ge\frac{-11}{2}$

Vậy $C_{min}=-\frac{11}{2}\Leftrightarrow2x-1=0\Leftrightarrow x=\frac{1}{2}$

và $\sqrt{10}y+\sqrt{\frac{5}{2}}=0\Leftrightarrow y\frac{-\sqrt{5}}{\sqrt{20}}=-0,5$

Câu trả lời:

$C=4x^2+10y-4x+10y-2$

$=\left(4x^2-4x+1\right)+\left(10y^2+10y+\frac{5}{2}\right)-\frac{11}{2}$

$=\left(2x-1\right)^2+\left(\sqrt{10y}+\sqrt{\frac{5}{2}}\right)^2-\frac{11}{2}\ge\frac{-11}{2}$

Vậy $C_{min}=-\frac{11}{2}\Leftrightarrow2x-1=0\Leftrightarrow x=\frac{1}{2}$

và $\sqrt{10}y+\sqrt{\frac{5}{2}}=0\Leftrightarrow y\frac{-\sqrt{5}}{\sqrt{20}}=-0,5$