已知xy-x-y=4,求(xy-1)^2-2x^2y-2xy^2+x^2+y^2+6xy-2x-2y的值
问题描述:
已知xy-x-y=4,求(xy-1)^2-2x^2y-2xy^2+x^2+y^2+6xy-2x-2y的值
答
对已知等式两侧平方,得x^2y^2+x^2+y^2-2x^2y-2xy^2+2xy = 16
所求 = x^2y^2-2xy+1-2x^2y-2xy^2+x^2+y^2+6xy-2x-2y = 16+2xy-2x-2y = 16+8 = 24