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设x,y∈R,比较(x*2+y*2)*2与xy(x+y)*2
人气:429 ℃ 时间:2020-05-14 23:23:28
解答
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...
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