Question

1. cho x-y=-10 và xy=-21 tính:

A=x^3-y^3

Answer 1

Ta có: \(xy=-21\)

\(\Leftrightarrow2xy=-42\)

Ta có: \(x-y=-10\)

\(\Leftrightarrow\left(x-y\right)^2=100\)

\(\Leftrightarrow x^2-2xy+y^2=100\)

\(\Leftrightarrow x^2+y^2-\left(-42\right)=100\)

\(\Leftrightarrow x^2+y^2+42=100\)

\(\Leftrightarrow x^2+y^2=58\)

Ta có: \(A=x^3-y^3\)

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

\(=-10\cdot\left[58+\left(-21\right)\right]\)

\(=-10\cdot\left[58-21\right]\)

\(=-10\cdot37=-370\)

Vậy: A=-370