Question

 tìm A :0

Answer 1

\(\dfrac{-x^2+2xy-y^2}{x+y}=\dfrac{A}{y^2-x^2}\)

\(\Leftrightarrow\dfrac{-\left(x-y\right)^2}{x+y}=\dfrac{A}{\left(y-x\right)\left(x+y\right)}\)

\(\Leftrightarrow-\left(x-y\right)^2=\dfrac{A}{y-x}\)

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

Answer 2

Theo đề bài, ta có:

-(x² - 2xy + y²)(y² - x²) = A(x + y)

⇔                   A(x + y) = (x² - 2xy + y²)(x + y)(x - y)

⇔                             A = (x - y)²(x - y)

⇔                            A = (x - y)³

Answer 3

\(\dfrac{-x^2+2xy-y^2}{x+y}=\dfrac{A}{y^2-x^2}\)

<=> \(\dfrac{-\left(-x^2+2xy-y^2\right)}{y+x}=\dfrac{A}{y^2-x^2}\)

<=> \(\dfrac{x^2-2xy+y^2}{y+x}=\dfrac{A}{y^2-x^2}\)

<=> \(\dfrac{\left(y-x\right)\left(x-y\right)^2}{y^2-x^2}=\dfrac{A}{y^2-x^2}\)

<=> A = (y - x)(x - y)²