\(A=\left(x+y\right)^2-8\left(x+y\right)+16-14\\ A=\left(x+y-4\right)^2-14\\ A=\left(5-4\right)^2-14=-13\)

\(A=x^2+2xy+y^2-8x-8y+2\)

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

\(=5^2-8.5+2\)

\(=-13\)

Vậy \(A=-13\) khi x + y = 5

Bạn xem lại đề

\(\Leftrightarrow\left(x^2-2xy+y^2\right)+8\left(x-y\right)+16=3-2y^2\)

\(\Leftrightarrow\left(x-y\right)^2+8\left(x-y\right)+16=3-2y^2\)

\(\Leftrightarrow\left(x-y+4\right)^2=3-2y^2\) (1)

Do \(\left(x-y+4\right)^2\ge0;\forall x,y\)

\(\Rightarrow3-2y^2\ge0\Rightarrow y^2\le\dfrac{3}{2}\Rightarrow\left[{}\begin{matrix}y^2=0\\y^2=1\end{matrix}\right.\)

\(\Rightarrow y=\left\{-1;0;1\right\}\)

- Với \(y=-1\) thay vào (1):

\(\left(x+5\right)^2=1\Rightarrow\left[{}\begin{matrix}x+5=1\\x+5=-1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-4\\x=-6\end{matrix}\right.\)

- Với \(y=1\) thay vào (1):

\(\Rightarrow\left(x+3\right)^2=1\Rightarrow\left[{}\begin{matrix}x+3=1\\x+3=-1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-2\\x=-4\end{matrix}\right.\)

- Với \(y=0\)

\(\Rightarrow\left(x+4\right)^2=3\) (ko có nghiệm nguyên do 3 ko phải SCP)

1) x² + xy-8x-8y

= x.(x+y) -8.(x+y)

= (x+y).(x-8)

2) 9x² -6x + 1 -36y²

=(3x-1)² -(6y)²

=(3x-1-6y)(3x-1+6y)

3)a² - b² -12a+12b

= (a-b)(a+b)-12.(a-b)

=(a-b).(a+b-12)

4)x² -2xy+8x-16y

=x.(x-2y)+8.(x-2y)

=(x-2y).(x+8)

5) x² -9y² +5x+15y

=(x-3y)(x+3y)+5.(x+3y)

= (x+3y).(x-3y+5)

\(1,x^2+xy-8x-8y=x\left(x+y\right)-8\left(x+y\right)=\left(x-8\right)\left(x+y\right)\)\(3,a^2-b^2-12a+12b=\left(a-b\right)\left(a+b\right)-12\left(a-b\right)=\left(a-b\right)\left(a+b-12\right)\)\(4,x^2-2xy+8x-16y=x\left(x-2y\right)+8\left(x-2y\right)=\left(x+8\right)\left(x-2y\right)\)\(5,x^2-9y^2+5x+15y=\left(x-3y\right)\left(x+3y\right)+5\left(x+3y\right)=\left(x+3y\right)\left(x-3y+5\right)\)

ko pt thông cảm nha

x² + y² = 8x + y + 8y + x

            = ( 8x + x ) + ( 8y + y)

            =       9x     +      9y

            =        9(x+y)

a) 3xy + x +15y +5

= (3xy + x) + (15y + 5)

= x(3y + 1) + 5(3y + 1)

= (3y + 1)(x + 5)

b) 9 - x² + 2xy - y²

= - [(-9) + (x² - 2xy + y² ) ]

= - [( -9) + (x - y)² ]

= 9 - (x - y)²

= 3² - ( x - y)²

= (3 - x +y)(3 + x - y)

e) x² - xy - 8x + 8y

= ( x² - xy ) - (8x - 8y)

= x(x -y) - 8(x-y)

= (x - y)(x - 8)

f) x² - 6x + 9 - y²

= (x² - 6x + 9) - y²

= (x - 3)² - y²

= (x - 3 -y)( x - 3 + y)

h) x² + 2xy +y² - yz

= (x² + 2xy +y² ) - yz

= (x+y)² - yz