Solution:

\(S=x^2-2xy+y^2-7x+7y+19\)

\(S=\left(x-y\right)^2-7\left(x-y\right)+19\)

\(S=5^2-7\cdot5+19\)

\(S=9\)

Vậy...

\(x^2-y^2+7x-7y=\left(x^2-y^2\right)+\left(7x-7y\right)=\left(x-y\right)\left(x+y\right)+7\left(x-y\right)=\left(x-y\right)\left(x+y+7\right)\)

\(x^2-10x+25-9y^2=\left(x^2-10x+25\right)-\left(3y\right)^2=\left(x-5\right)^2-\left(3y\right)^2=\left(x-3y-5\right)\left(x+3y-5\right)\)

\(x^2-y^2+7x-7y=\left(x-y\right)\left(x+y\right)+7\left(x-y\right)=\left(x-y\right)\left(x+y+7\right)\)

\(x^2-10x+25-9y^2=\left(x-5\right)^2-\left(3y\right)^2=\left(x-5-3y\right)\left(x-5+3y\right)\)

1. x² - 10x + 25 - 9y²

<=> x² - 10x + 5² - (3y)²

<=> (x - 5)² - (3y)²

<=> (x - 5 - 3y)(x - 5 + 3y)

2. x² - y² + 7x - 7y

<=> (x - y)(x + y) + 7(x - y)

<=> (x + y + 7)(x - y)

C

xy(x - y) - 7(x - y) = (x - y)(xy - 7)

Chọn đáp án B

⇒ Hệ phương trình đã cho vô nghiệm ⇒ S = ∅

Cách 2: Ta thấy:  ⇒ Hệ pt vô nghiệm

b: =x^3+2x^2-x^2+4

=x^2(x+2)-(x+2)(x-2)

=(x+2)(x^2-x+2)

c: =x^3-2x^2+x^2-4

=x^2(x-2)+(x-2)(x+2)

=(x-2)(x^2+x+2)

d: =(x-y)(x+y)-7(x+y)

=(x+y)(x-y-7)