设x,y∈R,比较(x*2+y*2)*2与xy(x+y)*2

题目

设x,y∈R,比较(x*2+y*2)*2与xy(x+y)*2

答案

作差法(x2+y2)2-xy(x+y)2=x＾4+y＾4+2x＾2y＾2-x＾3y-2x²y²－xy＾3=(x-y)(x＾3-y＾3)=(x-y)²[(x+y/2)^2+3y²/4]x=y则两式相等x≠y则(x-y)²＞0,(x+y/2)²+3y²2/4>0∴(x²+y&sup...