Question

1 tim gtln cua bieu thuc 

A=(x=1000)² +2y²-8y

Answer 1

Typo ? i think it \(A=\left(x+1000\right)^2+2y^2-8y\)

\(=\left(x+1000\right)^2+2y^2-8y+8-8\)

\(=\left(x+1000\right)^2+2\left(y^2-4y+4\right)-8\)

\(=\left(x+1000\right)^2+2\left(y-2\right)^2-8\)

Dễ thấy; \(\left(x+1000\right)^2\ge0;2\left(y-2\right)^2\ge0\)

\(\Rightarrow\left(x+1000\right)^2+2\left(y-2\right)^2\ge0\)

\(\Rightarrow\left(x+1000\right)^2+2\left(y-2\right)^2-8\ge-8\)

Xảy ra khi \(\left(x+1000\right)^2=0;2\left(y-2\right)^2=0\Rightarrow\hept{\begin{cases}x=-1000\\y=2\end{cases}}\)