已知xy=4满足想x²y-xy²-x+y=56.求x²+y²的值
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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