Question

Answer 1

Bài 5:

\(A=\left(-2x^2+4xy-2y^2\right)+4\left(x-y\right)-2-8y^2+8y-2+2020\\ A=-2\left[\left(x-y\right)^2-2\left(x-y\right)+1\right]-8\left(y^2-y+\dfrac{1}{4}\right)+2020\\ A=-2\left(x-y-1\right)^2-8\left(y-\dfrac{1}{2}\right)^2+2020\le2020\\ A_{max}=2020\Leftrightarrow\left\{{}\begin{matrix}x-y=1\\y=\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=\dfrac{1}{2}\end{matrix}\right.\)

Answer 2

Bài 3: 

a: Thay x=1 vào A, ta được:

\(A=1^3-9\cdot1^2+27\cdot1-27=1-9+27-27=-8\)