Question

[Nguyễn Hoàng Anh]

a) cho x-2y=-4;x.y=6. Tính x³ - 8y³

b)x+3y=10;x.y=3 .Tính x³+27y³

Answer 1

[Lấp La Lấp Lánh]

a) Ta có: \(x-2y=-4\Rightarrow\left(x-2y\right)^2=16\)

\(\Rightarrow x^2-4xy+4y^2=16\Rightarrow x^2+4y^2=16+4xy=16+4.6=40\)

\(x^3-8y^3=\left(x-2y\right)\left(x^2+2xy+4y^2\right)=\left(-4\right)\left(40+2.6\right)=-208\)

b) Ta có: \(x+3y=10\Rightarrow x^2+6xy+9y^2=100\Rightarrow x^2+9y^2=100-6xy=100-6.3=82\)

 \(x^3+27y^3=\left(x+3y\right)\left(x^2-3xy+9y^2\right)=10\left(82-3.3\right)=730\)