Question

若x〈y〈0,试比较(x2+y2)(x-y)与(x2-y2)(x+y)的大小 （x2是x平方） 急

Answer 1

(x2+y2)(x-y)-(x2-y2)(x+y) =(x2+y2)(x-y)-(x+y)^2(x-y) =(x-y)[x^2+y^2-(x+y)^2] =(x-y)(-2xy) 因为x〈y〈0 所以(x-y)(-2xy)＞0 即(x2+y2)(x-y)-(x2-y2)(x+y)＞0 所以(x2+y2)(x-y)＞(x2-y2)(x+y)