Question

若(x-1)(y+1)=3，xy(x-y)=4，求x的7次方减去y的7次方的值。

Answer 1

(x-1)(y+1)=xy+x-y-1=3，xy+(x-y)=4，xy(x-y)=4，xy=2，x-y=2，x²+y²=8，x³-y³=(x-y)(x²+xy+y²)=20，(x²+y²)(x³-y³)=160，x^5+x³y²-x²y³-y^5=x^5+x²y²(x-y)-y^5=x^5+8-y^5=160，x^5-y^5=152，(x²+y²)(x^5-y^5)=1216，x^7-y^7+x^5y²-x²y^5=x^7-y^7+x²y²(x³-y³)=x^7-y^7+80=1216，x^7-y^7=1136。