Question

1)Cho x + y = 11.Tính \(A=x^3+y^3+3xy\)

2) Cho x - y = 1. Tính \(B=x^3-y^3-3xy\)

Answer 1

1) \(A=x^3+y^3+3xy\)

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

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

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

Vậy A = 1.

Answer 2

2) \(B=x^3-y^3-3xy\)

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

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

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

\(B=\left(x-y\right)^2=1^2=1\)

Vậy B = 1.