试比较(x^2+y^2)(x-y)与(x^2-y^2)(x+y)的大小
问题描述:
试比较(x^2+y^2)(x-y)与(x^2-y^2)(x+y)的大小
答
(x^2+y^2)(x-y) = x^3 -x^2 *y + x * y^2 - y^3(x^2-y^2)(x+y) = x^3 +x^2 *y - x * y^2 - y^3故:(x^2+y^2)(x-y)-(x^2-y^2)(x+y)=(x^3 -x^2 *y + x * y^2 - y^3) - (x^3 +x^2 *y - x * y^2 - y^3) = -2x^2 *y +...