已知xy=4满足想x²y-xy²-x+y=56.求x²+y²的值

已知xy=4满足想x²y-xy²-x+y=56.求x²+y²的值
已知xy=4满足想x²y-xy²-x+y=56.求x²+y²的值

已知xy=4满足想x²y-xy²-x+y=56.求x²+y²的值
x²y-xy²-x+y
=xy(x-y)-(x-y)
=(xy-1)(x-y)
=56 xy=4
x-y=56/3
x²+y²=(x-y)^2+2xy=56^2/9+8

x²y-xy²-x+y=56 即：4x-4y-x+y=56。。整理得：3（x-y）=56。所以（x-y）=56/3
因为 （x-y）²=x²-2xy+y²
所以 x²+y²=（x-y）²+2xy=56/3的平方+8

x²y-xy²-x+y=xy(x-y)-(x-y)=(x-y)(xy-1),将xy=4带入，则有(x-y)=56/3;(x-y)的平方=x²+y²-2xy，将xy=4带入，则计算出x²+y²=（56/3）的平方-2乘4=（56/3）的平方-8