Question

1.a.Cho a+b=c. Tìm Mim A sao cho A=a^2+b^2
b. Cho x+2y = 8 tìm max B sao cho B= x.y
 

Answer 1

b. Theo giả thiết, ta có: \(x+2y=8\Rightarrow x=8-2y\)

Thay vào B, ta có:

\(B=\left(8-2y\right)y\)

\(=8y-2y^2\)

\(=8-2y^2+8y-8\)

\(=8-\left(2y^2-8y+8\right)\)

\(=8-2\left(y^2-4y+4\right)\)

\(=8-2\left(y-2\right)^2\le8\)

Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}y-2=0\\x+2y=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)

Vậy \(MaxB=8\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)