x³-y³+x²y-xy²=32
(x-y)(x²+xy+y²)+xy(x-y)=32
(x²+2xy+y²)(x-y)=32
(x+y)²(x-y)=32
∵（x+y)²≥0
∴(x-y)≥0
且x+y是正整數(shù)
32=2×16=4×8
當(dāng)x+y=4
x-y=2
x=3 y=1
當(dāng)x+y=2
x-y=8
x=5 y=-3
不符合題意
舍去
∴x=3 y=1