Question

[Nava Milim]

Cho x - y = 13x−y=13 và xy = 17.xy=17.

Giá trị biểu thức x^3 - y^3x3−y3 là

Answer 1

[Lấp La Lấp Lánh]

Ta có: \(x-y=13\)

\(\Rightarrow\left(x-y\right)^2=169\)

\(\Rightarrow x^2-2xy+y^2=169\)

\(\Rightarrow x^2+y^2=169+2xy=169+2.17=203\)

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

\(=13\left(203+17\right)=13.220=2860\)