Question

Tính A = x3 - 3xy - y3 biết x - y = 1

Answer 1

Tính

\(A=x^3-3xy-y^3\)

\(A=x^3-y^3-3xy\)

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

\(A=x^2+xy+y^2-3xy\)

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

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

\(A=1^2\)

\(A=1\)

Vậy A=1

Answer 2

\(A=x^3-3xy-y^3=x^3-3xy\left(x-y\right)-y^3\) ( vi x - y = 1)

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